tutorials.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning in Julia, JuliaCon2020"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A workshop introducing the machine learning toolbox\n",
    "[MLJ](https://alan-turing-institute.github.io/MLJ.jl/stable/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set-up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following instantiates a package environment and pre-loads some\n",
    "packages, to avoid delays later on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The package environment has been created using **Julia 1.6** and may not\n",
    "instantiate properly for other Julia versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "v\"1.6.3\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VERSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m environment at `~/Google Drive/Julia/MLJ/MachineLearningInJulia2020/Project.toml`\n",
      "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mInlineStrings\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mWeakRefStrings\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mScikitLearn\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39mCSV\n",
      "\u001b[32m  ✓ \u001b[39mMLJScikitLearnInterface\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mCorpusLoaders\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39mScientificTypes\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mOpenML\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39mMLJBase\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mMLJEnsembles\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mMLJIteration\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mMLJTuning\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39m\u001b[90mMLJSerialization\u001b[39m\n",
      "\u001b[32m  ✓ \u001b[39mMLJModels\n",
      "\u001b[32m  ✓ \u001b[39mMLJ\n",
      "  15 dependencies successfully precompiled in 46 seconds (231 already precompiled)\n",
      "┌ Info: Precompiling CSV [336ed68f-0bac-5ca0-87d4-7b16caf5d00b]\n",
      "└ @ Base loading.jl:1342\n",
      "┌ Info: Precompiling MLJ [add582a8-e3ab-11e8-2d5e-e98b27df1bc7]\n",
      "└ @ Base loading.jl:1342\n",
      "┌ Info: Precompiling MLJScikitLearnInterface [5ae90465-5518-4432-b9d2-8a1def2f0cab]\n",
      "└ @ Base loading.jl:1342\n",
      "┌ Info: Done loading\n",
      "└ @ Main /Users/anthony/Google Drive/Julia/MLJ/MachineLearningInJulia2020/setup.jl:27\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DIR = @__DIR__\n",
    "include(joinpath(DIR, \"setup.jl\"))\n",
    "color_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General resources"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [List of methods introduced in this tutorial](methods.md)\n",
    "- [MLJ Cheatsheet](https://alan-turing-institute.github.io/MLJ.jl/dev/mlj_cheatsheet/)\n",
    "- [Common MLJ Workflows](https://alan-turing-institute.github.io/MLJ.jl/dev/common_mlj_workflows/)\n",
    "- [MLJ manual](https://alan-turing-institute.github.io/MLJ.jl/dev/)\n",
    "- [Data Science Tutorials in Julia](https://juliaai.github.io/DataScienceTutorials.jl/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Part 1 - Data Representation](#part-1-data-representation)\n",
    "- [Part 2 - Selecting, Training and Evaluating Models](#part-2-selecting-training-and-evaluating-models)\n",
    "- [Part 3 - Transformers and Pipelines](#part-3-transformers-and-pipelines)\n",
    "- [Part 4 - Tuning Hyper-parameters](#part-4-tuning-hyper-parameters)\n",
    "- [Part 5 - Advanced model composition](#part-5-advanced-model-composition)\n",
    "- [Solutions to Exercises](#solutions-to-exercises)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part-1-data-representation'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1 - Data Representation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Goals:**\n",
    "> 1. Learn how MLJ specifies it's data requirements using \"scientific\" types\n",
    "> 2. Understand the options for representing tabular data\n",
    "> 3. Learn how to inspect and fix the representation of data to meet MLJ requirements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scientific types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To help you focus on the intended *purpose* or *interpretation* of\n",
    "data, MLJ models specify data requirements using *scientific types*,\n",
    "instead of machine types. An example of a scientific type is\n",
    "`OrderedFactor`. The other basic \"scalar\" scientific types are\n",
    "illustrated below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](assets/scitypes.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A scientific type is an ordinary Julia type (so it can be used for\n",
    "method dispatch, for example) but it usually has no instances. The\n",
    "`scitype` function is used to articulate MLJ's convention about how\n",
    "different machine types will be interpreted by MLJ models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Continuous"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using MLJ\n",
    "scitype(3.141)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Continuous} (alias for AbstractArray{Continuous, 1})"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time = [2.3, 4.5, 4.2, 1.8, 7.1]\n",
    "scitype(time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To fix data which MLJ is interpreting incorrectly, we use the\n",
    "`coerce` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Count} (alias for AbstractArray{Count, 1})"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "height = [185, 153, 163, 114, 180]\n",
    "scitype(height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Vector{Float64}:\n",
       " 185.0\n",
       " 153.0\n",
       " 163.0\n",
       " 114.0\n",
       " 180.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "height = coerce(height, Continuous)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of data we would want interpreted as\n",
    "`OrderedFactor` but isn't:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Union{Missing, Textual}} (alias for AbstractArray{Union{Missing, Textual}, 1})"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exam_mark = [\"rotten\", \"great\", \"bla\",  missing, \"great\"]\n",
    "scitype(exam_mark)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Trying to coerce from `Union{Missing, String}` to `OrderedFactor`.\n",
      "│ Coerced to `Union{Missing,OrderedFactor}` instead.\n",
      "└ @ ScientificTypes /Users/anthony/.julia/packages/ScientificTypes/z5Vmr/src/convention/coerce.jl:174\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5-element CategoricalArray{Union{Missing, String},1,UInt32}:\n",
       " \"rotten\"\n",
       " \"great\"\n",
       " \"bla\"\n",
       " missing\n",
       " \"great\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exam_mark = coerce(exam_mark, OrderedFactor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{String}:\n",
       " \"bla\"\n",
       " \"great\"\n",
       " \"rotten\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levels(exam_mark)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `levels!` to put the classes in the right order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levels!(exam_mark, [\"rotten\", \"bla\", \"great\"])\n",
    "exam_mark[1] < exam_mark[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When sub-sampling, no levels are lost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{String}:\n",
       " \"rotten\"\n",
       " \"bla\"\n",
       " \"great\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levels(exam_mark[1:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note on binary data.** There is no separate scientific type for\n",
    "binary data. Binary data is `OrderedFactor{2}` or\n",
    "`Multiclass{2}`. If a binary measure like `truepositive` is a\n",
    "applied to `OrderedFactor{2}` then the \"positive\" class is assumed\n",
    "to appear *second* in the ordering. If such a measure is applied to\n",
    "`Multiclass{2}` data, a warning is issued. A single `OrderedFactor`\n",
    "can be coerced to a single `Continuous` variable, for models that\n",
    "require this, while a `Multiclass` variable can only be one-hot\n",
    "encoded."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-dimensional data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever it makes sense, MLJ Models generally expect two-dimensional\n",
    "data to be *tabular*. All the tabular formats implementing the\n",
    "[Tables.jl API](https://juliadata.github.io/Tables.jl/stable/) (see\n",
    "this\n",
    "[list](https://github.com/JuliaData/Tables.jl/blob/master/INTEGRATIONS.md))\n",
    "have a scientific type of `Table` and can be used with such models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probably the simplest example of a table is the julia native *column\n",
    "table*, which is just a named tuple of equal-length vectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(h = [185.0, 153.0, 163.0, 114.0, 180.0],\n",
       " e = Union{Missing, CategoricalValue{String, UInt32}}[\"rotten\", \"great\", \"bla\", missing, \"great\"],\n",
       " t = [2.3, 4.5, 4.2, 1.8, 7.1],)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_table = (h=height, e=exam_mark, t=time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Table{Union{AbstractVector{Union{Missing, OrderedFactor{3}}}, AbstractVector{Continuous}}}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(column_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the `Table{K}` type parameter `K` encodes the scientific\n",
    "types of the columns. (This is useful when comparing table scitypes\n",
    "with `<:`). To inspect the individual column scitypes, we use the\n",
    "`schema` method instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────┬──────────────────────────────────────────────────┬──────────────────\n",
       "│\u001b[22m _.names \u001b[0m│\u001b[22m _.types                                          \u001b[0m│\u001b[22m _.scitypes     \u001b[0m ⋯\n",
       "├─────────┼──────────────────────────────────────────────────┼──────────────────\n",
       "│ h       │ Float64                                          │ Continuous      ⋯\n",
       "│ e       │ Union{Missing, CategoricalValue{String, UInt32}} │ Union{Missing,  ⋯\n",
       "│ t       │ Float64                                          │ Continuous      ⋯\n",
       "└─────────┴──────────────────────────────────────────────────┴──────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n",
       "_.nrows = 5\n"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schema(column_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are five other examples of tables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────┬──────────────────────────────────────────────────┬──────────────────\n",
       "│\u001b[22m _.names \u001b[0m│\u001b[22m _.types                                          \u001b[0m│\u001b[22m _.scitypes     \u001b[0m ⋯\n",
       "├─────────┼──────────────────────────────────────────────────┼──────────────────\n",
       "│ e       │ Union{Missing, CategoricalValue{String, UInt32}} │ Union{Missing,  ⋯\n",
       "│ h       │ Float64                                          │ Continuous      ⋯\n",
       "│ t       │ Float64                                          │ Continuous      ⋯\n",
       "└─────────┴──────────────────────────────────────────────────┴──────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n",
       "_.nrows = 5\n"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict_table = Dict(:h => height, :e => exam_mark, :t => time)\n",
    "schema(dict_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(To control column order here, instead use `LittleDict` from\n",
    "OrderedCollections.jl.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├─────────┼─────────┼────────────┤\n",
       "│ a       │ Int64   │ Count      │\n",
       "│ b       │ Float64 │ Continuous │\n",
       "└─────────┴─────────┴────────────┘\n",
       "_.nrows = 3\n"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_table = [(a=1, b=3.4),\n",
    "             (a=2, b=4.5),\n",
    "             (a=3, b=5.6)]\n",
    "schema(row_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 3 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>h</th><th>e</th><th>t</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Union{Missing, CategoricalValue{String, UInt32}}\">Cat…?</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>185.0</td><td>rotten</td><td>2.3</td></tr><tr><th>2</th><td>153.0</td><td>great</td><td>4.5</td></tr><tr><th>3</th><td>163.0</td><td>bla</td><td>4.2</td></tr><tr><th>4</th><td>114.0</td><td><em>missing</em></td><td>1.8</td></tr><tr><th>5</th><td>180.0</td><td>great</td><td>7.1</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& h & e & t\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Cat…? & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 185.0 & rotten & 2.3 \\\\\n",
       "\t2 & 153.0 & great & 4.5 \\\\\n",
       "\t3 & 163.0 & bla & 4.2 \\\\\n",
       "\t4 & 114.0 & \\emph{missing} & 1.8 \\\\\n",
       "\t5 & 180.0 & great & 7.1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m h       \u001b[0m\u001b[1m e       \u001b[0m\u001b[1m t       \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Float64 \u001b[0m\u001b[90m Cat…?   \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼───────────────────────────\n",
       "   1 │   185.0  rotten       2.3\n",
       "   2 │   153.0  great        4.5\n",
       "   3 │   163.0  bla          4.2\n",
       "   4 │   114.0 \u001b[90m missing \u001b[0m     1.8\n",
       "   5 │   180.0  great        7.1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import DataFrames\n",
    "df = DataFrames.DataFrame(column_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schema(df) == schema(column_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├─────────────────────────┼─────────┼────────────┤\n",
       "│ surgery                 │ Int64   │ Count      │\n",
       "│ age                     │ Int64   │ Count      │\n",
       "│ rectal_temperature      │ Float64 │ Continuous │\n",
       "│ pulse                   │ Int64   │ Count      │\n",
       "│ respiratory_rate        │ Int64   │ Count      │\n",
       "│ temperature_extremities │ Int64   │ Count      │\n",
       "│ mucous_membranes        │ Int64   │ Count      │\n",
       "│ capillary_refill_time   │ Int64   │ Count      │\n",
       "│ pain                    │ Int64   │ Count      │\n",
       "│ peristalsis             │ Int64   │ Count      │\n",
       "│ abdominal_distension    │ Int64   │ Count      │\n",
       "│ packed_cell_volume      │ Float64 │ Continuous │\n",
       "│ total_protein           │ Float64 │ Continuous │\n",
       "│ outcome                 │ Int64   │ Count      │\n",
       "│ surgical_lesion         │ Int64   │ Count      │\n",
       "│ cp_data                 │ Int64   │ Count      │\n",
       "└─────────────────────────┴─────────┴────────────┘\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CSV\n",
    "file = CSV.File(joinpath(DIR, \"data\", \"horse.csv\"));\n",
    "schema(file) # (triggers a file read)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most MLJ models do not accept matrix in lieu of a table, but you can\n",
    "wrap a matrix as a table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├─────────┼─────────┼────────────┤\n",
       "│ x1      │ Float64 │ Continuous │\n",
       "│ x2      │ Float64 │ Continuous │\n",
       "│ x3      │ Float64 │ Continuous │\n",
       "└─────────┴─────────┴────────────┘\n",
       "_.nrows = 2\n"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_table = MLJ.table(rand(2,3))\n",
    "schema(matrix_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrix is *not* copied, only wrapped. Some models may perform\n",
    "better if one wraps the adjoint of the transpose - see\n",
    "[here](https://alan-turing-institute.github.io/MLJ.jl/dev/getting_started/#Observations-correspond-to-rows,-not-columns)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Manipulating tabular data.** In this workshop we assume\n",
    "familiarity with some kind of tabular data container (although it is\n",
    "possible, in principle, to carry out the exercises without this.)\n",
    "For a quick start introduction to `DataFrames`, see [this\n",
    "tutorial](https://juliaai.github.io/DataScienceTutorials.jl/data/dataframe/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixing scientific types in tabular data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To show how we can correct the scientific types of data in tables,\n",
    "we introduce a cleaned up version of the UCI Horse Colic Data Set\n",
    "(the cleaning work-flow is described\n",
    "[here](https://juliaai.github.io/DataScienceTutorials.jl/end-to-end/horse/#dealing_with_missing_values))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>4 rows × 16 columns (omitted printing of 10 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>surgery</th><th>age</th><th>rectal_temperature</th><th>pulse</th><th>respiratory_rate</th><th>temperature_extremities</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>2</td><td>1</td><td>38.5</td><td>66</td><td>66</td><td>3</td></tr><tr><th>2</th><td>1</td><td>1</td><td>39.2</td><td>88</td><td>88</td><td>3</td></tr><tr><th>3</th><td>2</td><td>1</td><td>38.3</td><td>40</td><td>40</td><td>1</td></tr><tr><th>4</th><td>1</td><td>9</td><td>39.1</td><td>164</td><td>164</td><td>4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& surgery & age & rectal\\_temperature & pulse & respiratory\\_rate & temperature\\_extremities & \\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64 & Int64 & Int64 & Int64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 2 & 1 & 38.5 & 66 & 66 & 3 & $\\dots$ \\\\\n",
       "\t2 & 1 & 1 & 39.2 & 88 & 88 & 3 & $\\dots$ \\\\\n",
       "\t3 & 2 & 1 & 38.3 & 40 & 40 & 1 & $\\dots$ \\\\\n",
       "\t4 & 1 & 9 & 39.1 & 164 & 164 & 4 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×16 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m surgery \u001b[0m\u001b[1m age   \u001b[0m\u001b[1m rectal_temperature \u001b[0m\u001b[1m pulse \u001b[0m\u001b[1m respiratory_rate \u001b[0m\u001b[1m temperatur\u001b[0m ⋯\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64   \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64            \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64            \u001b[0m\u001b[90m Int64     \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │       2      1                38.5     66                66             ⋯\n",
       "   2 │       1      1                39.2     88                88\n",
       "   3 │       2      1                38.3     40                40\n",
       "   4 │       1      9                39.1    164               164\n",
       "\u001b[36m                                                              11 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CSV\n",
    "file = CSV.File(joinpath(DIR, \"data\", \"horse.csv\"));\n",
    "horse = DataFrames.DataFrame(file); # convert to data frame without copying columns\n",
    "first(horse, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From [the UCI\n",
    "docs](http://archive.ics.uci.edu/ml/datasets/Horse+Colic) we can\n",
    "surmise how each variable ought to be interpreted (a step in our\n",
    "work-flow that cannot reliably be left to the computer):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "variable                    | scientific type (interpretation)\n",
    "----------------------------|-----------------------------------\n",
    "`:surgery`                  | Multiclass\n",
    "`:age`                      | Multiclass\n",
    "`:rectal_temperature`       | Continuous\n",
    "`:pulse`                    | Continuous\n",
    "`:respiratory_rate`         | Continuous\n",
    "`:temperature_extremities`  | OrderedFactor\n",
    "`:mucous_membranes`         | Multiclass\n",
    "`:capillary_refill_time`    | Multiclass\n",
    "`:pain`                     | OrderedFactor\n",
    "`:peristalsis`              | OrderedFactor\n",
    "`:abdominal_distension`     | OrderedFactor\n",
    "`:packed_cell_volume`       | Continuous\n",
    "`:total_protein`            | Continuous\n",
    "`:outcome`                  | Multiclass\n",
    "`:surgical_lesion`          | OrderedFactor\n",
    "`:cp_data`                  | Multiclass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how MLJ will actually interpret the data, as it is\n",
    "currently encoded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├─────────────────────────┼─────────┼────────────┤\n",
       "│ surgery                 │ Int64   │ Count      │\n",
       "│ age                     │ Int64   │ Count      │\n",
       "│ rectal_temperature      │ Float64 │ Continuous │\n",
       "│ pulse                   │ Int64   │ Count      │\n",
       "│ respiratory_rate        │ Int64   │ Count      │\n",
       "│ temperature_extremities │ Int64   │ Count      │\n",
       "│ mucous_membranes        │ Int64   │ Count      │\n",
       "│ capillary_refill_time   │ Int64   │ Count      │\n",
       "│ pain                    │ Int64   │ Count      │\n",
       "│ peristalsis             │ Int64   │ Count      │\n",
       "│ abdominal_distension    │ Int64   │ Count      │\n",
       "│ packed_cell_volume      │ Float64 │ Continuous │\n",
       "│ total_protein           │ Float64 │ Continuous │\n",
       "│ outcome                 │ Int64   │ Count      │\n",
       "│ surgical_lesion         │ Int64   │ Count      │\n",
       "│ cp_data                 │ Int64   │ Count      │\n",
       "└─────────────────────────┴─────────┴────────────┘\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schema(horse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a first correction step, we can get MLJ to \"guess\" the\n",
    "appropriate fix, using the `autotype` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Symbol, Type} with 11 entries:\n",
       "  :abdominal_distension    => OrderedFactor\n",
       "  :pain                    => OrderedFactor\n",
       "  :surgery                 => OrderedFactor\n",
       "  :mucous_membranes        => OrderedFactor\n",
       "  :surgical_lesion         => OrderedFactor\n",
       "  :outcome                 => OrderedFactor\n",
       "  :capillary_refill_time   => OrderedFactor\n",
       "  :age                     => OrderedFactor\n",
       "  :temperature_extremities => OrderedFactor\n",
       "  :peristalsis             => OrderedFactor\n",
       "  :cp_data                 => OrderedFactor"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "autotype(horse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, this is not perfect, but a step in the right direction, which\n",
    "we implement like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────────────────────────────┬───────────────────\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types                         \u001b[0m│\u001b[22m _.scitypes      \u001b[0m ⋯\n",
       "├─────────────────────────┼─────────────────────────────────┼───────────────────\n",
       "│ surgery                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ age                     │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ rectal_temperature      │ Float64                         │ Continuous       ⋯\n",
       "│ pulse                   │ Int64                           │ Count            ⋯\n",
       "│ respiratory_rate        │ Int64                           │ Count            ⋯\n",
       "│ temperature_extremities │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ mucous_membranes        │ CategoricalValue{Int64, UInt32} │ OrderedFactor{6} ⋯\n",
       "│ capillary_refill_time   │ CategoricalValue{Int64, UInt32} │ OrderedFactor{3} ⋯\n",
       "│ pain                    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{5} ⋯\n",
       "│ peristalsis             │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ abdominal_distension    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ packed_cell_volume      │ Float64                         │ Continuous       ⋯\n",
       "│ total_protein           │ Float64                         │ Continuous       ⋯\n",
       "│ outcome                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{3} ⋯\n",
       "│ surgical_lesion         │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ cp_data                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "└─────────────────────────┴─────────────────────────────────┴───────────────────\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(horse, autotype(horse));\n",
    "schema(horse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All remaining `Count` data should be `Continuous`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────────────────────────────┬───────────────────\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types                         \u001b[0m│\u001b[22m _.scitypes      \u001b[0m ⋯\n",
       "├─────────────────────────┼─────────────────────────────────┼───────────────────\n",
       "│ surgery                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ age                     │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ rectal_temperature      │ Float64                         │ Continuous       ⋯\n",
       "│ pulse                   │ Float64                         │ Continuous       ⋯\n",
       "│ respiratory_rate        │ Float64                         │ Continuous       ⋯\n",
       "│ temperature_extremities │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ mucous_membranes        │ CategoricalValue{Int64, UInt32} │ OrderedFactor{6} ⋯\n",
       "│ capillary_refill_time   │ CategoricalValue{Int64, UInt32} │ OrderedFactor{3} ⋯\n",
       "│ pain                    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{5} ⋯\n",
       "│ peristalsis             │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ abdominal_distension    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ packed_cell_volume      │ Float64                         │ Continuous       ⋯\n",
       "│ total_protein           │ Float64                         │ Continuous       ⋯\n",
       "│ outcome                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{3} ⋯\n",
       "│ surgical_lesion         │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ cp_data                 │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "└─────────────────────────┴─────────────────────────────────┴───────────────────\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(horse, Count => Continuous);\n",
    "schema(horse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll correct the remaining truant entries manually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────────────────────────────┬───────────────────\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types                         \u001b[0m│\u001b[22m _.scitypes      \u001b[0m ⋯\n",
       "├─────────────────────────┼─────────────────────────────────┼───────────────────\n",
       "│ surgery                 │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "│ age                     │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "│ rectal_temperature      │ Float64                         │ Continuous       ⋯\n",
       "│ pulse                   │ Float64                         │ Continuous       ⋯\n",
       "│ respiratory_rate        │ Float64                         │ Continuous       ⋯\n",
       "│ temperature_extremities │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ mucous_membranes        │ CategoricalValue{Int64, UInt32} │ Multiclass{6}    ⋯\n",
       "│ capillary_refill_time   │ CategoricalValue{Int64, UInt32} │ Multiclass{3}    ⋯\n",
       "│ pain                    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{5} ⋯\n",
       "│ peristalsis             │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ abdominal_distension    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ packed_cell_volume      │ Float64                         │ Continuous       ⋯\n",
       "│ total_protein           │ Float64                         │ Continuous       ⋯\n",
       "│ outcome                 │ CategoricalValue{Int64, UInt32} │ Multiclass{3}    ⋯\n",
       "│ surgical_lesion         │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ cp_data                 │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "└─────────────────────────┴─────────────────────────────────┴───────────────────\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(horse,\n",
    "        :surgery               => Multiclass,\n",
    "        :age                   => Multiclass,\n",
    "        :mucous_membranes      => Multiclass,\n",
    "        :capillary_refill_time => Multiclass,\n",
    "        :outcome               => Multiclass,\n",
    "        :cp_data               => Multiclass);\n",
    "schema(horse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resources for Part 1\n",
    "\n",
    "- From the MLJ manual:\n",
    "   - [A preview of data type specification in\n",
    "  MLJ](https://alan-turing-institute.github.io/MLJ.jl/dev/getting_started/#A-preview-of-data-type-specification-in-MLJ-1)\n",
    "   - [Data containers and scientific types](https://alan-turing-institute.github.io/MLJ.jl/dev/getting_started/#Data-containers-and-scientific-types-1)\n",
    "   - [Working with Categorical Data](https://alan-turing-institute.github.io/MLJ.jl/dev/working_with_categorical_data/)\n",
    "- [Summary](https://juliaai.github.io/ScientificTypes.jl/dev/#Summary-of-the-default-convention) of the MLJ convention for representing scientific types\n",
    "- [ScientificTypes.jl](https://juliaai.github.io/ScientificTypes.jl/dev/)\n",
    "- From Data Science Tutorials:\n",
    "    - [Data interpretation: Scientific Types](https://juliaai.github.io/DataScienceTutorials.jl/data/scitype/)\n",
    "    - [Horse colic data](https://juliaai.github.io/DataScienceTutorials.jl/end-to-end/horse/)\n",
    "- [UCI Horse Colic Data Set](http://archive.ics.uci.edu/ml/datasets/Horse+Colic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises for Part 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try to guess how each code snippet below will evaluate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Count"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Textual} (alias for AbstractArray{Textual, 1})"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "questions = [\"who\", \"why\", \"what\", \"when\"]\n",
    "scitype(questions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Textual"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elscitype(questions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Tuple{Continuous, Count, Textual}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = (3.141, 42, \"how\")\n",
    "scitype(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 0.578566  0.0280166  0.974146\n",
       " 0.518531  0.910351   0.796979"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractMatrix{Continuous} (alias for AbstractArray{Continuous, 2})"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Continuous"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elscitype(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 SparseMatrixCSC{Float64, Int64} with 6 stored entries:\n",
       " 0.578566  0.0280166  0.974146\n",
       " 0.518531  0.910351   0.796979"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using SparseArrays\n",
    "Asparse = sparse(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractMatrix{Continuous} (alias for AbstractArray{Continuous, 2})"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(Asparse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 CategoricalArray{Float64,2,UInt32}:\n",
       " 0.578566  0.0280166  0.974146\n",
       " 0.518531  0.910351   0.796979"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CategoricalArrays\n",
    "C1 = categorical(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractMatrix{Multiclass{6}} (alias for AbstractArray{Multiclass{6}, 2})"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(C1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Multiclass{6}"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elscitype(C1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractMatrix{OrderedFactor{6}} (alias for AbstractArray{OrderedFactor{6}, 2})"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C2 = categorical(A, ordered=true)\n",
    "scitype(C2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Union{Missing, Count}} (alias for AbstractArray{Union{Missing, Count}, 1})"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [1, 2, missing, 4]\n",
    "scitype(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Union{Missing, Count}"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elscitype(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Union{Missing, Count}} (alias for AbstractArray{Union{Missing, Count}, 1})"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(v[1:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can you guess at the general behavior of\n",
    "`scitype` with respect to tuples, abstract arrays and missing\n",
    "values? The answers are\n",
    "[here](https://github.com/juliaai/ScientificTypesBase.jl#2-the-scitype-and-scitype-methods)\n",
    "(ignore \"Property 1\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coerce the following vector to make MLJ recognize it as a vector of\n",
    "ordered factors (with an appropriate ordering):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Vector{Union{Missing, String}}:\n",
       " \"good\"\n",
       " \"poor\"\n",
       " \"poor\"\n",
       " \"excellent\"\n",
       " missing\n",
       " \"good\"\n",
       " \"excellent\""
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quality = [\"good\", \"poor\", \"poor\", \"excellent\", missing, \"good\", \"excellent\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3 (fixing scitypes in a table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fix the scitypes for the [House Prices in King\n",
    "County](https://mlr3gallery.mlr-org.com/posts/2020-01-30-house-prices-in-king-county/)\n",
    "dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>4 rows × 19 columns (omitted printing of 11 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>price</th><th>bedrooms</th><th>bathrooms</th><th>sqft_living</th><th>sqft_lot</th><th>floors</th><th>waterfront</th><th>view</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>221900.0</td><td>3</td><td>1.0</td><td>1180</td><td>5650</td><td>1.0</td><td>0</td><td>0</td></tr><tr><th>2</th><td>538000.0</td><td>3</td><td>2.25</td><td>2570</td><td>7242</td><td>2.0</td><td>0</td><td>0</td></tr><tr><th>3</th><td>180000.0</td><td>2</td><td>1.0</td><td>770</td><td>10000</td><td>1.0</td><td>0</td><td>0</td></tr><tr><th>4</th><td>604000.0</td><td>4</td><td>3.0</td><td>1960</td><td>5000</td><td>1.0</td><td>0</td><td>0</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& price & bedrooms & bathrooms & sqft\\_living & sqft\\_lot & floors & waterfront & view & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Int64 & Float64 & Int64 & Int64 & Float64 & Int64 & Int64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 221900.0 & 3 & 1.0 & 1180 & 5650 & 1.0 & 0 & 0 & $\\dots$ \\\\\n",
       "\t2 & 538000.0 & 3 & 2.25 & 2570 & 7242 & 2.0 & 0 & 0 & $\\dots$ \\\\\n",
       "\t3 & 180000.0 & 2 & 1.0 & 770 & 10000 & 1.0 & 0 & 0 & $\\dots$ \\\\\n",
       "\t4 & 604000.0 & 4 & 3.0 & 1960 & 5000 & 1.0 & 0 & 0 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×19 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m price    \u001b[0m\u001b[1m bedrooms \u001b[0m\u001b[1m bathrooms \u001b[0m\u001b[1m sqft_living \u001b[0m\u001b[1m sqft_lot \u001b[0m\u001b[1m floors  \u001b[0m\u001b[1m waterfro\u001b[0m ⋯\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Float64  \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64   \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ 221900.0         3       1.0          1180      5650      1.0           ⋯\n",
       "   2 │ 538000.0         3       2.25         2570      7242      2.0\n",
       "   3 │ 180000.0         2       1.0           770     10000      1.0\n",
       "   4 │ 604000.0         4       3.0          1960      5000      1.0\n",
       "\u001b[36m                                                              13 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = CSV.File(joinpath(DIR, \"data\", \"house.csv\"));\n",
    "house = DataFrames.DataFrame(file); # convert to data frame without copying columns\n",
    "first(house, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Two features in the original data set have been deemed uninformative\n",
    "and dropped, namely `:id` and `:date`. The original feature\n",
    "`:yr_renovated` has been replaced by the `Bool` feature `is_renovated`.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part-2-selecting-training-and-evaluating-models'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2 - Selecting, Training and Evaluating Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Goals:**\n",
    "> 1. Search MLJ's database of model metadata to identify model candidates for a supervised learning task.\n",
    "> 2. Evaluate the performance of a model on a holdout set using basic `fit!`/`predict` work-flow.\n",
    "> 3. Inspect the outcomes of training and save these to a file.\n",
    "> 3. Evaluate performance using other resampling strategies, such as cross-validation, in one line, using `evaluate!`\n",
    "> 4. Plot a \"learning curve\", to inspect performance as a function of some model hyper-parameter, such as an iteration parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"Hello World!\" of machine learning is to classify Fisher's\n",
    "famous iris data set. This time, we'll grab the data from\n",
    "[OpenML](https://www.openml.org):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\textbf{Author}: R.A. Fisher   \\textbf{Source}: \\href{https://archive.ics.uci.edu/ml/datasets/Iris}{UCI} - 1936 - Donated by Michael Marshall   \\textbf{Please cite}:   \n",
       "\n",
       "\\textbf{Iris Plants Database}   This is perhaps the best known database to be found in the pattern recognition literature.  Fisher's paper is a classic in the field and is referenced frequently to this day.  (See Duda \\& Hart, for example.)  The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant.  One class is     linearly separable from the other 2; the latter are NOT linearly separable from each other.\n",
       "\n",
       "Predicted attribute: class of iris plant.   This is an exceedingly simple domain.  \n",
       "\n",
       "\\subsubsection{Attribute Information:}\n",
       "\\begin{verbatim}\n",
       "1. sepal length in cm\n",
       "2. sepal width in cm\n",
       "3. petal length in cm\n",
       "4. petal width in cm\n",
       "5. class: \n",
       "   -- Iris Setosa\n",
       "   -- Iris Versicolour\n",
       "   -- Iris Virginica\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "**Author**: R.A. Fisher   **Source**: [UCI](https://archive.ics.uci.edu/ml/datasets/Iris) - 1936 - Donated by Michael Marshall   **Please cite**:   \n",
       "\n",
       "**Iris Plants Database**   This is perhaps the best known database to be found in the pattern recognition literature.  Fisher's paper is a classic in the field and is referenced frequently to this day.  (See Duda & Hart, for example.)  The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant.  One class is     linearly separable from the other 2; the latter are NOT linearly separable from each other.\n",
       "\n",
       "Predicted attribute: class of iris plant.   This is an exceedingly simple domain.  \n",
       "\n",
       "### Attribute Information:\n",
       "\n",
       "```\n",
       "1. sepal length in cm\n",
       "2. sepal width in cm\n",
       "3. petal length in cm\n",
       "4. petal width in cm\n",
       "5. class: \n",
       "   -- Iris Setosa\n",
       "   -- Iris Versicolour\n",
       "   -- Iris Virginica\n",
       "```\n"
      ],
      "text/plain": [
       "  \u001b[1mAuthor\u001b[22m: R.A. Fisher \u001b[1mSource\u001b[22m: UCI\n",
       "  (https://archive.ics.uci.edu/ml/datasets/Iris) - 1936 - Donated by Michael\n",
       "  Marshall \u001b[1mPlease cite\u001b[22m:\n",
       "\n",
       "  \u001b[1mIris Plants Database\u001b[22m This is perhaps the best known database to be found in\n",
       "  the pattern recognition literature. Fisher's paper is a classic in the field\n",
       "  and is referenced frequently to this day. (See Duda & Hart, for example.)\n",
       "  The data set contains 3 classes of 50 instances each, where each class\n",
       "  refers to a type of iris plant. One class is linearly separable from the\n",
       "  other 2; the latter are NOT linearly separable from each other.\n",
       "\n",
       "  Predicted attribute: class of iris plant. This is an exceedingly simple\n",
       "  domain.\n",
       "\n",
       "\u001b[1m  Attribute Information:\u001b[22m\n",
       "\u001b[1m  ––––––––––––––––––––––––\u001b[22m\n",
       "\n",
       "\u001b[36m  1. sepal length in cm\u001b[39m\n",
       "\u001b[36m  2. sepal width in cm\u001b[39m\n",
       "\u001b[36m  3. petal length in cm\u001b[39m\n",
       "\u001b[36m  4. petal width in cm\u001b[39m\n",
       "\u001b[36m  5. class: \u001b[39m\n",
       "\u001b[36m     -- Iris Setosa\u001b[39m\n",
       "\u001b[36m     -- Iris Versicolour\u001b[39m\n",
       "\u001b[36m     -- Iris Virginica\u001b[39m"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OpenML.describe_dataset(61)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>4 rows × 5 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>sepallength</th><th>sepalwidth</th><th>petallength</th><th>petalwidth</th><th>class</th></tr><tr><th></th><th title=\"Union{Missing, Float64}\">Float64?</th><th title=\"Union{Missing, Float64}\">Float64?</th><th title=\"Union{Missing, Float64}\">Float64?</th><th title=\"Union{Missing, Float64}\">Float64?</th><th title=\"Union{Missing, CategoricalValue{String, UInt32}}\">Cat…?</th></tr></thead><tbody><tr><th>1</th><td>5.1</td><td>3.5</td><td>1.4</td><td>0.2</td><td>Iris-setosa</td></tr><tr><th>2</th><td>4.9</td><td>3.0</td><td>1.4</td><td>0.2</td><td>Iris-setosa</td></tr><tr><th>3</th><td>4.7</td><td>3.2</td><td>1.3</td><td>0.2</td><td>Iris-setosa</td></tr><tr><th>4</th><td>4.6</td><td>3.1</td><td>1.5</td><td>0.2</td><td>Iris-setosa</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& sepallength & sepalwidth & petallength & petalwidth & class\\\\\n",
       "\t\\hline\n",
       "\t& Float64? & Float64? & Float64? & Float64? & Cat…?\\\\\n",
       "\t\\hline\n",
       "\t1 & 5.1 & 3.5 & 1.4 & 0.2 & Iris-setosa \\\\\n",
       "\t2 & 4.9 & 3.0 & 1.4 & 0.2 & Iris-setosa \\\\\n",
       "\t3 & 4.7 & 3.2 & 1.3 & 0.2 & Iris-setosa \\\\\n",
       "\t4 & 4.6 & 3.1 & 1.5 & 0.2 & Iris-setosa \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m sepallength \u001b[0m\u001b[1m sepalwidth \u001b[0m\u001b[1m petallength \u001b[0m\u001b[1m petalwidth \u001b[0m\u001b[1m class       \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Float64?    \u001b[0m\u001b[90m Float64?   \u001b[0m\u001b[90m Float64?    \u001b[0m\u001b[90m Float64?   \u001b[0m\u001b[90m Cat…?       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────\n",
       "   1 │         5.1         3.5          1.4         0.2  Iris-setosa\n",
       "   2 │         4.9         3.0          1.4         0.2  Iris-setosa\n",
       "   3 │         4.7         3.2          1.3         0.2  Iris-setosa\n",
       "   4 │         4.6         3.1          1.5         0.2  Iris-setosa"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = OpenML.load(61); # a row table\n",
    "iris = DataFrames.DataFrame(iris);\n",
    "first(iris, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Main goal.** To build and evaluate models for predicting the\n",
    "`:class` variable, given the four remaining measurement variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1. Inspect and fix scientific types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────┬──────────────────────────────────────────────────┬──────────────\n",
       "│\u001b[22m _.names     \u001b[0m│\u001b[22m _.types                                          \u001b[0m│\u001b[22m _.scitypes \u001b[0m ⋯\n",
       "├─────────────┼──────────────────────────────────────────────────┼──────────────\n",
       "│ sepallength │ Union{Missing, Float64}                          │ Union{Missi ⋯\n",
       "│ sepalwidth  │ Union{Missing, Float64}                          │ Union{Missi ⋯\n",
       "│ petallength │ Union{Missing, Float64}                          │ Union{Missi ⋯\n",
       "│ petalwidth  │ Union{Missing, Float64}                          │ Union{Missi ⋯\n",
       "│ class       │ Union{Missing, CategoricalValue{String, UInt32}} │ Union{Missi ⋯\n",
       "└─────────────┴──────────────────────────────────────────────────┴──────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n",
       "_.nrows = 150\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schema(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately, `Missing` is appearing in the element type, despite\n",
    "the fact there are no missing values (see this\n",
    "[issue](https://github.com/JuliaAI/OpenML.jl/issues/10)). To do this\n",
    "we have to explicilty tighten the types:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────┬──────────────────────────────────┬───────────────┐\n",
       "│\u001b[22m _.names     \u001b[0m│\u001b[22m _.types                          \u001b[0m│\u001b[22m _.scitypes    \u001b[0m│\n",
       "├─────────────┼──────────────────────────────────┼───────────────┤\n",
       "│ sepallength │ Float64                          │ Continuous    │\n",
       "│ sepalwidth  │ Float64                          │ Continuous    │\n",
       "│ petallength │ Float64                          │ Continuous    │\n",
       "│ petalwidth  │ Float64                          │ Continuous    │\n",
       "│ class       │ CategoricalValue{String, UInt32} │ Multiclass{3} │\n",
       "└─────────────┴──────────────────────────────────┴───────────────┘\n",
       "_.nrows = 150\n"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(iris,\n",
    "        Union{Missing,Continuous}=>Continuous,\n",
    "        Union{Missing,Multiclass}=>Multiclass,\n",
    "        tight=true)\n",
    "schema(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2. Split data into input and target parts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how we split the data into target and input features, which\n",
    "is needed for MLJ supervised models. We randomize the data at the\n",
    "same time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{Multiclass{3}} (alias for AbstractArray{Multiclass{3}, 1})"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = unpack(iris, ==(:class), name->true; rng=123);\n",
    "scitype(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's one way to access the documentation (at the REPL, `?unpack`\n",
    "also works):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "t1, t2, ...., tk = unpack(table, f1, f2, ... fk;\n",
       "                         wrap_singles=false,\n",
       "                         shuffle=false,\n",
       "                         rng::Union{AbstractRNG,Int,Nothing}=nothing)\n",
       "\\end{verbatim}\n",
       "Horizontally split any Tables.jl compatible \\texttt{table} into smaller tables (or vectors) \\texttt{t1, t2, ..., tk} by making column selections \\textbf{without replacement} by successively applying the columnn name filters \\texttt{f1}, \\texttt{f2}, ..., \\texttt{fk}. A \\emph{filter} is any object \\texttt{f} such that \\texttt{f(name)} is \\texttt{true} or \\texttt{false} for each column \\texttt{name::Symbol} of \\texttt{table}. For example, use the filter \\texttt{\\_ -> true} to pick up all remaining columns of the table.\n",
       "\n",
       "Whenever a returned table contains a single column, it is converted to a vector unless \\texttt{wrap\\_singles=true}.\n",
       "\n",
       "Scientific type conversions can be optionally specified (note semicolon):\n",
       "\n",
       "\\begin{verbatim}\n",
       "unpack(table, t...; col1=>scitype1, col2=>scitype2, ... )\n",
       "\\end{verbatim}\n",
       "If \\texttt{shuffle=true} then the rows of \\texttt{table} are first shuffled, using the global RNG, unless \\texttt{rng} is specified; if \\texttt{rng} is an integer, it specifies the seed of an automatically generated Mersenne twister. If \\texttt{rng} is specified then \\texttt{shuffle=true} is implicit.\n",
       "\n",
       "\\subsubsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> table = DataFrame(x=[1,2], y=['a', 'b'], z=[10.0, 20.0], w=[\"A\", \"B\"])\n",
       "julia> Z, XY = unpack(table, ==(:z), !=(:w);\n",
       "               :x=>Continuous, :y=>Multiclass)\n",
       "julia> XY\n",
       "2×2 DataFrame\n",
       "│ Row │ x       │ y            │\n",
       "│     │ Float64 │ Categorical… │\n",
       "├─────┼─────────┼──────────────┤\n",
       "│ 1   │ 1.0     │ 'a'          │\n",
       "│ 2   │ 2.0     │ 'b'          │\n",
       "\n",
       "julia> Z\n",
       "2-element Array{Float64,1}:\n",
       " 10.0\n",
       " 20.0\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "t1, t2, ...., tk = unpack(table, f1, f2, ... fk;\n",
       "                         wrap_singles=false,\n",
       "                         shuffle=false,\n",
       "                         rng::Union{AbstractRNG,Int,Nothing}=nothing)\n",
       "```\n",
       "\n",
       "Horizontally split any Tables.jl compatible `table` into smaller tables (or vectors) `t1, t2, ..., tk` by making column selections **without replacement** by successively applying the columnn name filters `f1`, `f2`, ..., `fk`. A *filter* is any object `f` such that `f(name)` is `true` or `false` for each column `name::Symbol` of `table`. For example, use the filter `_ -> true` to pick up all remaining columns of the table.\n",
       "\n",
       "Whenever a returned table contains a single column, it is converted to a vector unless `wrap_singles=true`.\n",
       "\n",
       "Scientific type conversions can be optionally specified (note semicolon):\n",
       "\n",
       "```\n",
       "unpack(table, t...; col1=>scitype1, col2=>scitype2, ... )\n",
       "```\n",
       "\n",
       "If `shuffle=true` then the rows of `table` are first shuffled, using the global RNG, unless `rng` is specified; if `rng` is an integer, it specifies the seed of an automatically generated Mersenne twister. If `rng` is specified then `shuffle=true` is implicit.\n",
       "\n",
       "### Example\n",
       "\n",
       "```\n",
       "julia> table = DataFrame(x=[1,2], y=['a', 'b'], z=[10.0, 20.0], w=[\"A\", \"B\"])\n",
       "julia> Z, XY = unpack(table, ==(:z), !=(:w);\n",
       "               :x=>Continuous, :y=>Multiclass)\n",
       "julia> XY\n",
       "2×2 DataFrame\n",
       "│ Row │ x       │ y            │\n",
       "│     │ Float64 │ Categorical… │\n",
       "├─────┼─────────┼──────────────┤\n",
       "│ 1   │ 1.0     │ 'a'          │\n",
       "│ 2   │ 2.0     │ 'b'          │\n",
       "\n",
       "julia> Z\n",
       "2-element Array{Float64,1}:\n",
       " 10.0\n",
       " 20.0\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  t1, t2, ...., tk = unpack(table, f1, f2, ... fk;\u001b[39m\n",
       "\u001b[36m                           wrap_singles=false,\u001b[39m\n",
       "\u001b[36m                           shuffle=false,\u001b[39m\n",
       "\u001b[36m                           rng::Union{AbstractRNG,Int,Nothing}=nothing)\u001b[39m\n",
       "\n",
       "  Horizontally split any Tables.jl compatible \u001b[36mtable\u001b[39m into smaller tables (or\n",
       "  vectors) \u001b[36mt1, t2, ..., tk\u001b[39m by making column selections \u001b[1mwithout replacement\u001b[22m by\n",
       "  successively applying the columnn name filters \u001b[36mf1\u001b[39m, \u001b[36mf2\u001b[39m, ..., \u001b[36mfk\u001b[39m. A \u001b[4mfilter\u001b[24m is\n",
       "  any object \u001b[36mf\u001b[39m such that \u001b[36mf(name)\u001b[39m is \u001b[36mtrue\u001b[39m or \u001b[36mfalse\u001b[39m for each column \u001b[36mname::Symbol\u001b[39m\n",
       "  of \u001b[36mtable\u001b[39m. For example, use the filter \u001b[36m_ -> true\u001b[39m to pick up all remaining\n",
       "  columns of the table.\n",
       "\n",
       "  Whenever a returned table contains a single column, it is converted to a\n",
       "  vector unless \u001b[36mwrap_singles=true\u001b[39m.\n",
       "\n",
       "  Scientific type conversions can be optionally specified (note semicolon):\n",
       "\n",
       "\u001b[36m  unpack(table, t...; col1=>scitype1, col2=>scitype2, ... )\u001b[39m\n",
       "\n",
       "  If \u001b[36mshuffle=true\u001b[39m then the rows of \u001b[36mtable\u001b[39m are first shuffled, using the global\n",
       "  RNG, unless \u001b[36mrng\u001b[39m is specified; if \u001b[36mrng\u001b[39m is an integer, it specifies the seed of\n",
       "  an automatically generated Mersenne twister. If \u001b[36mrng\u001b[39m is specified then\n",
       "  \u001b[36mshuffle=true\u001b[39m is implicit.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  –––––––––\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> table = DataFrame(x=[1,2], y=['a', 'b'], z=[10.0, 20.0], w=[\"A\", \"B\"])\u001b[39m\n",
       "\u001b[36m  julia> Z, XY = unpack(table, ==(:z), !=(:w);\u001b[39m\n",
       "\u001b[36m                 :x=>Continuous, :y=>Multiclass)\u001b[39m\n",
       "\u001b[36m  julia> XY\u001b[39m\n",
       "\u001b[36m  2×2 DataFrame\u001b[39m\n",
       "\u001b[36m  │ Row │ x       │ y            │\u001b[39m\n",
       "\u001b[36m  │     │ Float64 │ Categorical… │\u001b[39m\n",
       "\u001b[36m  ├─────┼─────────┼──────────────┤\u001b[39m\n",
       "\u001b[36m  │ 1   │ 1.0     │ 'a'          │\u001b[39m\n",
       "\u001b[36m  │ 2   │ 2.0     │ 'b'          │\u001b[39m\n",
       "\u001b[36m  \u001b[39m\n",
       "\u001b[36m  julia> Z\u001b[39m\n",
       "\u001b[36m  2-element Array{Float64,1}:\u001b[39m\n",
       "\u001b[36m   10.0\u001b[39m\n",
       "\u001b[36m   20.0\u001b[39m"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc unpack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On searching for a model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how to see *all* models (not immediately useful):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "183-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = ABODDetector, package_name = OutlierDetectionNeighbors, ... )\n",
       " (name = ABODDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = AEDetector, package_name = OutlierDetectionNetworks, ... )\n",
       " (name = ARDRegressor, package_name = ScikitLearn, ... )\n",
       " (name = AdaBoostClassifier, package_name = ScikitLearn, ... )\n",
       " (name = AdaBoostRegressor, package_name = ScikitLearn, ... )\n",
       " (name = AdaBoostStumpClassifier, package_name = DecisionTree, ... )\n",
       " (name = AffinityPropagation, package_name = ScikitLearn, ... )\n",
       " (name = AgglomerativeClustering, package_name = ScikitLearn, ... )\n",
       " (name = BaggingClassifier, package_name = ScikitLearn, ... )\n",
       " (name = BaggingRegressor, package_name = ScikitLearn, ... )\n",
       " (name = BayesianLDA, package_name = MultivariateStats, ... )\n",
       " (name = BayesianLDA, package_name = ScikitLearn, ... )\n",
       " ⋮\n",
       " (name = Standardizer, package_name = MLJModels, ... )\n",
       " (name = SubspaceLDA, package_name = MultivariateStats, ... )\n",
       " (name = TSVDTransformer, package_name = TSVD, ... )\n",
       " (name = TheilSenRegressor, package_name = ScikitLearn, ... )\n",
       " (name = UnivariateBoxCoxTransformer, package_name = MLJModels, ... )\n",
       " (name = UnivariateDiscretizer, package_name = MLJModels, ... )\n",
       " (name = UnivariateFillImputer, package_name = MLJModels, ... )\n",
       " (name = UnivariateStandardizer, package_name = MLJModels, ... )\n",
       " (name = UnivariateTimeTypeToContinuous, package_name = MLJModels, ... )\n",
       " (name = XGBoostClassifier, package_name = XGBoost, ... )\n",
       " (name = XGBoostCount, package_name = XGBoost, ... )\n",
       " (name = XGBoostRegressor, package_name = XGBoost, ... )"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_models = models()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each entry contains metadata for a model whose defining code is not yet loaded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AEDetector from OutlierDetectionNetworks.jl.\n",
       "[Documentation](https://github.com/OutlierDetectionJL/OutlierDetectionNetworks.jl).\n",
       "(name = \"AEDetector\",\n",
       " package_name = \"OutlierDetectionNetworks\",\n",
       " is_supervised = false,\n",
       " abstract_type = MLJModelInterface.UnsupervisedDetector,\n",
       " deep_properties = (),\n",
       " docstring = \"AEDetector from OutlierDetectionNetworks.jl.\\n[Documentation](https://github.com/OutlierDetectionJL/OutlierDetectionNetworks.jl).\",\n",
       " fit_data_scitype = Tuple{Union{Table{_s52} where _s52<:(AbstractVector{_s51} where _s51<:Continuous), AbstractMatrix{_s689} where _s689<:Continuous}},\n",
       " hyperparameter_ranges = (nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing),\n",
       " hyperparameter_types = (\"Flux.Chain\", \"Flux.Chain\", \"Integer\", \"Integer\", \"Bool\", \"Bool\", \"Any\", \"Function\"),\n",
       " hyperparameters = (:encoder, :decoder, :batchsize, :epochs, :shuffle, :partial, :opt, :loss),\n",
       " implemented_methods = [:clean!, :fit, :transform],\n",
       " inverse_transform_scitype = Unknown,\n",
       " is_pure_julia = true,\n",
       " is_wrapper = false,\n",
       " iteration_parameter = nothing,\n",
       " load_path = \"OutlierDetectionNetworks.AEDetector\",\n",
       " package_license = \"MIT\",\n",
       " package_url = \"https://github.com/OutlierDetectionJL/OutlierDetectionNetworks.jl\",\n",
       " package_uuid = \"c7f57e37-4fcb-4a0b-a36c-c2204bc839a7\",\n",
       " predict_scitype = Unknown,\n",
       " prediction_type = :unknown,\n",
       " supports_class_weights = false,\n",
       " supports_online = false,\n",
       " supports_training_losses = false,\n",
       " supports_weights = false,\n",
       " transform_scitype = AbstractVector{_s689} where _s689<:Continuous,\n",
       " input_scitype = Union{Table{_s52} where _s52<:(AbstractVector{_s51} where _s51<:Continuous), AbstractMatrix{_s689} where _s689<:Continuous},\n",
       " target_scitype = AbstractVector{_s689} where _s689<:Union{Missing, OrderedFactor{2}},\n",
       " output_scitype = AbstractVector{_s689} where _s689<:Continuous,)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meta = all_models[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AbstractVector{_s689} where _s689<:Union{Missing, OrderedFactor{2}} (alias for AbstractArray{_s689, 1} where _s689<:Union{Missing, OrderedFactor{2}})"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "targetscitype = meta.target_scitype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scitype(y) <: targetscitype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this model won't do. Let's  find all pure julia classifiers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = AdaBoostStumpClassifier, package_name = DecisionTree, ... )\n",
       " (name = BayesianLDA, package_name = MultivariateStats, ... )\n",
       " (name = BayesianSubspaceLDA, package_name = MultivariateStats, ... )\n",
       " (name = ConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = DecisionTreeClassifier, package_name = BetaML, ... )\n",
       " (name = DecisionTreeClassifier, package_name = DecisionTree, ... )\n",
       " (name = DeterministicConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = EvoTreeClassifier, package_name = EvoTrees, ... )\n",
       " (name = GaussianNBClassifier, package_name = NaiveBayes, ... )\n",
       " (name = KNNClassifier, package_name = NearestNeighborModels, ... )\n",
       " (name = KernelPerceptronClassifier, package_name = BetaML, ... )\n",
       " (name = LDA, package_name = MultivariateStats, ... )\n",
       " (name = LogisticClassifier, package_name = MLJLinearModels, ... )\n",
       " (name = MultinomialClassifier, package_name = MLJLinearModels, ... )\n",
       " (name = MultinomialNBClassifier, package_name = NaiveBayes, ... )\n",
       " (name = NeuralNetworkClassifier, package_name = MLJFlux, ... )\n",
       " (name = PegasosClassifier, package_name = BetaML, ... )\n",
       " (name = PerceptronClassifier, package_name = BetaML, ... )\n",
       " (name = RandomForestClassifier, package_name = BetaML, ... )\n",
       " (name = RandomForestClassifier, package_name = DecisionTree, ... )\n",
       " (name = SubspaceLDA, package_name = MultivariateStats, ... )"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filter_julia_classifiers(meta) =\n",
    "    AbstractVector{Finite} <: meta.target_scitype &&\n",
    "    meta.is_pure_julia\n",
    "\n",
    "models(filter_julia_classifiers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find all models with \"Classifier\" in `name` (or `docstring`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = AdaBoostClassifier, package_name = ScikitLearn, ... )\n",
       " (name = AdaBoostStumpClassifier, package_name = DecisionTree, ... )\n",
       " (name = BaggingClassifier, package_name = ScikitLearn, ... )\n",
       " (name = BernoulliNBClassifier, package_name = ScikitLearn, ... )\n",
       " (name = ComplementNBClassifier, package_name = ScikitLearn, ... )\n",
       " (name = ConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = DecisionTreeClassifier, package_name = BetaML, ... )\n",
       " (name = DecisionTreeClassifier, package_name = DecisionTree, ... )\n",
       " (name = DeterministicConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = DummyClassifier, package_name = ScikitLearn, ... )\n",
       " (name = EvoTreeClassifier, package_name = EvoTrees, ... )\n",
       " (name = ExtraTreesClassifier, package_name = ScikitLearn, ... )\n",
       " (name = GaussianNBClassifier, package_name = NaiveBayes, ... )\n",
       " ⋮\n",
       " (name = PerceptronClassifier, package_name = ScikitLearn, ... )\n",
       " (name = ProbabilisticSGDClassifier, package_name = ScikitLearn, ... )\n",
       " (name = RandomForestClassifier, package_name = BetaML, ... )\n",
       " (name = RandomForestClassifier, package_name = DecisionTree, ... )\n",
       " (name = RandomForestClassifier, package_name = ScikitLearn, ... )\n",
       " (name = RidgeCVClassifier, package_name = ScikitLearn, ... )\n",
       " (name = RidgeClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SGDClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVMClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVMLinearClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVMNuClassifier, package_name = ScikitLearn, ... )\n",
       " (name = XGBoostClassifier, package_name = XGBoost, ... )"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models(\"Classifier\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find all (supervised) models that match my data!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = AdaBoostClassifier, package_name = ScikitLearn, ... )\n",
       " (name = AdaBoostStumpClassifier, package_name = DecisionTree, ... )\n",
       " (name = BaggingClassifier, package_name = ScikitLearn, ... )\n",
       " (name = BayesianLDA, package_name = MultivariateStats, ... )\n",
       " (name = BayesianLDA, package_name = ScikitLearn, ... )\n",
       " (name = BayesianQDA, package_name = ScikitLearn, ... )\n",
       " (name = BayesianSubspaceLDA, package_name = MultivariateStats, ... )\n",
       " (name = ConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = DecisionTreeClassifier, package_name = BetaML, ... )\n",
       " (name = DecisionTreeClassifier, package_name = DecisionTree, ... )\n",
       " (name = DeterministicConstantClassifier, package_name = MLJModels, ... )\n",
       " (name = DummyClassifier, package_name = ScikitLearn, ... )\n",
       " (name = EvoTreeClassifier, package_name = EvoTrees, ... )\n",
       " ⋮\n",
       " (name = RandomForestClassifier, package_name = BetaML, ... )\n",
       " (name = RandomForestClassifier, package_name = DecisionTree, ... )\n",
       " (name = RandomForestClassifier, package_name = ScikitLearn, ... )\n",
       " (name = RidgeCVClassifier, package_name = ScikitLearn, ... )\n",
       " (name = RidgeClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SGDClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVC, package_name = LIBSVM, ... )\n",
       " (name = SVMClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVMLinearClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SVMNuClassifier, package_name = ScikitLearn, ... )\n",
       " (name = SubspaceLDA, package_name = MultivariateStats, ... )\n",
       " (name = XGBoostClassifier, package_name = XGBoost, ... )"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models(matching(X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3. Select and instantiate a model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To load the code defining a new model type we use the `@load` macro:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJFlux ✔\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLJFlux.NeuralNetworkClassifier"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NeuralNetworkClassifier = @load NeuralNetworkClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other ways to load model code are described\n",
    "[here](https://alan-turing-institute.github.io/MLJ.jl/dev/loading_model_code/#Loading-Model-Code)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll instantiate this type with default values for the\n",
    "hyperparameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NeuralNetworkClassifier(\n",
       "    builder = Short(\n",
       "            n_hidden = 0,\n",
       "            dropout = 0.5,\n",
       "            σ = NNlib.σ),\n",
       "    finaliser = NNlib.softmax,\n",
       "    optimiser = Flux.Optimise.ADAM(0.001, (0.9, 0.999), IdDict{Any, Any}()),\n",
       "    loss = Flux.Losses.crossentropy,\n",
       "    epochs = 10,\n",
       "    batch_size = 1,\n",
       "    lambda = 0.0,\n",
       "    alpha = 0.0,\n",
       "    rng = Random._GLOBAL_RNG(),\n",
       "    optimiser_changes_trigger_retraining = false,\n",
       "    acceleration = CPU1{Nothing}(nothing))"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = NeuralNetworkClassifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A neural network model for making probabilistic predictions of a `Multiclass` or `OrderedFactor` target, given a table of `Continuous` features. \n",
       "→ based on [MLJFlux](https://github.com/alan-turing-institute/MLJFlux.jl).\n",
       "→ do `@load NeuralNetworkClassifier pkg=\"MLJFlux\"` to use the model.\n",
       "→ do `?NeuralNetworkClassifier` for documentation.\n",
       "(name = \"NeuralNetworkClassifier\",\n",
       " package_name = \"MLJFlux\",\n",
       " is_supervised = true,\n",
       " abstract_type = Probabilistic,\n",
       " deep_properties = (:optimiser, :builder),\n",
       " docstring = \"A neural network model for making probabilistic predictions of a `Multiclass` or `OrderedFactor` target, given a table of `Continuous` features. \\n→ based on [MLJFlux](https://github.com/alan-turing-institute/MLJFlux.jl).\\n→ do `@load NeuralNetworkClassifier pkg=\\\"MLJFlux\\\"` to use the model.\\n→ do `?NeuralNetworkClassifier` for documentation.\",\n",
       " fit_data_scitype = Tuple{Table{var\"#s53\"} where var\"#s53\"<:(AbstractVector{var\"#s52\"} where var\"#s52\"<:Continuous), AbstractVector{var\"#s76\"} where var\"#s76\"<:Finite},\n",
       " hyperparameter_ranges = (nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing),\n",
       " hyperparameter_types = (\"MLJFlux.Short\", \"typeof(NNlib.softmax)\", \"Flux.Optimise.ADAM\", \"typeof(Flux.Losses.crossentropy)\", \"Int64\", \"Int64\", \"Float64\", \"Float64\", \"Union{Int64, Random.AbstractRNG}\", \"Bool\", \"ComputationalResources.AbstractResource\"),\n",
       " hyperparameters = (:builder, :finaliser, :optimiser, :loss, :epochs, :batch_size, :lambda, :alpha, :rng, :optimiser_changes_trigger_retraining, :acceleration),\n",
       " implemented_methods = Any[],\n",
       " inverse_transform_scitype = Unknown,\n",
       " is_pure_julia = true,\n",
       " is_wrapper = false,\n",
       " iteration_parameter = :epochs,\n",
       " load_path = \"MLJFlux.NeuralNetworkClassifier\",\n",
       " package_license = \"MIT\",\n",
       " package_url = \"https://github.com/alan-turing-institute/MLJFlux.jl\",\n",
       " package_uuid = \"094fc8d1-fd35-5302-93ea-dabda2abf845\",\n",
       " predict_scitype = AbstractVector{ScientificTypesBase.Density{_s25} where _s25<:Finite},\n",
       " prediction_type = :probabilistic,\n",
       " supports_class_weights = false,\n",
       " supports_online = false,\n",
       " supports_training_losses = true,\n",
       " supports_weights = false,\n",
       " transform_scitype = Unknown,\n",
       " input_scitype = Table{var\"#s53\"} where var\"#s53\"<:(AbstractVector{var\"#s52\"} where var\"#s52\"<:Continuous),\n",
       " target_scitype = AbstractVector{var\"#s76\"} where var\"#s76\"<:Finite,\n",
       " output_scitype = Unknown,)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "info(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In MLJ a *model* is just a struct containing hyper-parameters, and\n",
    "that's all. A model does not store *learned* parameters. Models are\n",
    "mutable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.epochs = 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all models have a key-word constructor that works once `@load`\n",
    "has been performed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NeuralNetworkClassifier(epochs=12) == model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On fitting, predicting, and inspecting models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In MLJ a model and training/validation data are typically bound\n",
    "together in a machine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 0 times; caches data\n",
       "  args: \n",
       "    1:\tSource @429 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @444 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach = machine(model, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A machine stores *learned* parameters, among other things. We'll\n",
    "train this machine on 70% of the data and evaluate on a 30% holdout\n",
    "set. Let's start by dividing all row indices into `train` and `test`\n",
    "subsets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  96, 97, 98, 99, 100, 101, 102, 103, 104, 105], [106, 107, 108, 109, 110, 111, 112, 113, 114, 115  …  141, 142, 143, 144, 145, 146, 147, 148, 149, 150])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train, test = partition(eachindex(y), 0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can `fit!`..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Loss is 1.132\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.08\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.068\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.033\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.029\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9917\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.01\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.005\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 1.003\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.989\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9486\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9571\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 1 time; caches data\n",
       "  args: \n",
       "    1:\tSource @429 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @444 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit!(mach, rows=train, verbosity=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and `predict`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element MLJBase.UnivariateFiniteVector{Multiclass{3}, String, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.277, Iris-versicolor=>0.366, Iris-virginica=>0.357)\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.251, Iris-versicolor=>0.376, Iris-virginica=>0.373)\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.494, Iris-versicolor=>0.278, Iris-virginica=>0.227)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = predict(mach, rows=test);  # or `predict(mach, Xnew)`\n",
    "yhat[1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll have more to say on the form of this prediction shortly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After training, one can inspect the learned parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(chain = Chain(Chain(Dense(4, 3, σ), Dropout(0.5), Dense(3, 3)), softmax),)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_params(mach)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Everything else the user might be interested in is accessed from the\n",
    "training *report*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(training_losses = [1.085632308348892, 1.1320773531582096, 1.0799144410260113, 1.0684055699601498, 1.0326802305670144, 1.0286735172997612, 0.9916782091001018, 1.0103330144134601, 1.0052723608475305, 1.0032265584476034, 0.9890359632792628, 0.9486166278543674, 0.9570811840979994],)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "report(mach)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You save a machine like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "MLJ.save(\"neural_net.jlso\", mach)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And retrieve it like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element MLJBase.UnivariateFiniteVector{Multiclass{3}, String, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.223, Iris-versicolor=>0.377, Iris-virginica=>0.4)\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.283, Iris-versicolor=>0.366, Iris-virginica=>0.351)\n",
       " UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.245, Iris-versicolor=>0.38, Iris-virginica=>0.374)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach2 = machine(\"neural_net.jlso\")\n",
    "yhat = predict(mach2, X);\n",
    "yhat[1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to fit a retrieved model, you will need to bind some data to it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "\u001b[33mOptimising neural net:100%[=========================] Time: 0:00:00\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 2 times; caches data\n",
       "  args: \n",
       "    1:\tSource @960 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @704 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach3 = machine(\"neural_net.jlso\", X, y)\n",
    "fit!(mach3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Machines remember the last set of hyper-parameters used during fit,\n",
    "which, in the case of iterative models, allows for a warm restart of\n",
    "computations in the case that only the iteration parameter is\n",
    "increased:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Loss is 0.8915\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8667\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8937\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9132\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 2 times; caches data\n",
       "  args: \n",
       "    1:\tSource @429 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @444 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.epochs = model.epochs + 4\n",
    "fit!(mach, rows=train, verbosity=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this particular model we can also increase `:learning_rate`\n",
    "without triggering a cold restart:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Loss is 0.7963\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7339\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7615\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.6521\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 3 times; caches data\n",
       "  args: \n",
       "    1:\tSource @429 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @444 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.epochs = model.epochs + 4\n",
    "model.optimiser.eta = 10*model.optimiser.eta\n",
    "fit!(mach, rows=train, verbosity=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, change any other parameter and training will restart from\n",
    "scratch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Loss is 1.189\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9707\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9315\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8361\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8291\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7744\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.817\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7495\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8286\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7549\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7823\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.9084\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7369\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.8187\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7275\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7538\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.72\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.7105\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.6554\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n",
      "┌ Info: Loss is 0.6316\n",
      "└ @ MLJFlux /Users/anthony/.julia/packages/MLJFlux/5ENQA/src/core.jl:128\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{NeuralNetworkClassifier{Short,…},…} trained 4 times; caches data\n",
       "  args: \n",
       "    1:\tSource @429 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @444 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.lambda = 0.001\n",
    "fit!(mach, rows=train, verbosity=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Iterative models that implement warm-restart for training can be\n",
    "controlled externally (eg, using an out-of-sample stopping\n",
    "criterion). See\n",
    "[here](https://alan-turing-institute.github.io/MLJ.jl/dev/controlling_iterative_models/)\n",
    "for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train silently for a total of 50 epochs, and look at a\n",
    "prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "\u001b[33mOptimising neural net:100%[=========================] Time: 0:00:01\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "UnivariateFinite{Multiclass{3}}(Iris-setosa=>0.0815, Iris-versicolor=>0.491, Iris-virginica=>0.428)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.epochs = 50\n",
    "fit!(mach, rows=train)\n",
    "yhat = predict(mach, X[test,:]); # or predict(mach, rows=test)\n",
    "yhat[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What's going on here?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":probabilistic"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "info(model).prediction_type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Important**:\n",
    "- In MLJ, a model that can predict probabilities (and not just point values) will do so by default.\n",
    "- For most probabilistic predictors, the predicted object is a `Distributions.Distribution` object, supporting the `Distributions.jl` [API](https://juliastats.org/Distributions.jl/latest/extends/#Create-a-Distribution-1) for such objects. In particular, the methods `rand`,  `pdf`, `logpdf`, `mode`, `median` and `mean` will apply, where appropriate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, to obtain the probability of \"Iris-virginica\" in the first test\n",
    "prediction, we do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4278096647438517"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdf(yhat[1], \"Iris-virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the most likely observation, we do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CategoricalValue{String, UInt32} \"Iris-versicolor\""
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mode(yhat[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These can be broadcast over multiple predictions in the usual way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{Float64}:\n",
       " 0.4906890545157449\n",
       " 0.4263386756761465\n",
       " 0.03496101759113145\n",
       " 0.40529054408497234"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "broadcast(pdf, yhat[1:4], \"Iris-versicolor\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element CategoricalArray{String,1,UInt32}:\n",
       " \"Iris-versicolor\"\n",
       " \"Iris-virginica\"\n",
       " \"Iris-setosa\"\n",
       " \"Iris-virginica\""
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mode.(yhat[1:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, alternatively, you can use the `predict_mode` operation instead\n",
    "of `predict`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element CategoricalArray{String,1,UInt32}:\n",
       " \"Iris-versicolor\"\n",
       " \"Iris-virginica\"\n",
       " \"Iris-setosa\"\n",
       " \"Iris-virginica\""
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict_mode(mach, X[test,:])[1:4] # or predict_mode(mach, rows=test)[1:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a more conventional matrix of probabilities you can do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×3 Matrix{Float64}:\n",
       " 0.0815013  0.490689  0.42781\n",
       " 0.0565988  0.426339  0.517062\n",
       " 0.965022   0.034961  1.68514e-5\n",
       " 0.050214   0.405291  0.544495"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = levels(y)\n",
    "pdf(yhat, L)[1:4, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, in a typical MLJ work-flow, this is not as useful as you\n",
    "might imagine. In particular, all probabilistic performance measures\n",
    "in MLJ expect distribution objects in their first slot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46064123289626785"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy(yhat, y[test]) |> mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To apply a deterministic measure, we first need to obtain point-estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15555555555555556"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "misclassification_rate(mode.(yhat), y[test])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note in passing that there is also a search tool for measures\n",
    "analogous to `models`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61-element Vector{NamedTuple{(:name, :instances, :human_name, :target_scitype, :supports_weights, :supports_class_weights, :prediction_type, :orientation, :reports_each_observation, :aggregation, :is_feature_dependent, :docstring, :distribution_type), T} where T<:Tuple}:\n",
       " (name = BrierLoss, instances = [brier_loss], ...)\n",
       " (name = BrierScore, instances = [brier_score], ...)\n",
       " (name = LPLoss, instances = [l1, l2], ...)\n",
       " (name = LogCoshLoss, instances = [log_cosh, log_cosh_loss], ...)\n",
       " (name = LogLoss, instances = [log_loss, cross_entropy], ...)\n",
       " (name = LogScore, instances = [log_score], ...)\n",
       " (name = SphericalScore, instances = [spherical_score], ...)\n",
       " (name = Accuracy, instances = [accuracy], ...)\n",
       " (name = AreaUnderCurve, instances = [area_under_curve, auc], ...)\n",
       " (name = BalancedAccuracy, instances = [balanced_accuracy, bacc, bac], ...)\n",
       " (name = ConfusionMatrix, instances = [confusion_matrix, confmat], ...)\n",
       " (name = FScore, instances = [f1score], ...)\n",
       " (name = FalseDiscoveryRate, instances = [false_discovery_rate, falsediscovery_rate, fdr], ...)\n",
       " ⋮\n",
       " (name = ModifiedHuberLoss, instances = [modified_huber_loss], ...)\n",
       " (name = PerceptronLoss, instances = [perceptron_loss], ...)\n",
       " (name = SigmoidLoss, instances = [sigmoid_loss], ...)\n",
       " (name = SmoothedL1HingeLoss, instances = [smoothed_l1_hinge_loss], ...)\n",
       " (name = ZeroOneLoss, instances = [zero_one_loss], ...)\n",
       " (name = HuberLoss, instances = [huber_loss], ...)\n",
       " (name = L1EpsilonInsLoss, instances = [l1_epsilon_ins_loss], ...)\n",
       " (name = L2EpsilonInsLoss, instances = [l2_epsilon_ins_loss], ...)\n",
       " (name = LPDistLoss, instances = [lp_dist_loss], ...)\n",
       " (name = LogitDistLoss, instances = [logit_dist_loss], ...)\n",
       " (name = PeriodicLoss, instances = [periodic_loss], ...)\n",
       " (name = QuantileLoss, instances = [quantile_loss], ...)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measures()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4. Evaluate the model performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturally, MLJ provides boilerplate code for carrying out a model\n",
    "evaluation with a lot less fuss. Let's repeat the performance\n",
    "evaluation above and add an extra measure, `brier_score`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬──────────┐\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold \u001b[0m│\n",
       "├────────────────────────────┼─────────────┼───────────┼──────────┤\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.461       │ predict   │ [0.461]  │\n",
       "│ BrierScore()               │ -0.286      │ predict   │ [-0.286] │\n",
       "└────────────────────────────┴─────────────┴───────────┴──────────┘\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate!(mach, resampling=Holdout(fraction_train=0.7),\n",
    "          measures=[cross_entropy, brier_score])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or applying cross-validation instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:24\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬────────────────────────\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├────────────────────────────┼─────────────┼───────────┼────────────────────────\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.381       │ predict   │ [0.4, 0.342, 0.399, 0 ⋯\n",
       "│ BrierScore()               │ -0.206      │ predict   │ [-0.222, -0.181, -0.2 ⋯\n",
       "└────────────────────────────┴─────────────┴───────────┴────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate!(mach, resampling=CV(nfolds=6),\n",
    "          measures=[cross_entropy, brier_score])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, Monte Carlo cross-validation (cross-validation repeated\n",
    "randomized folds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 18 folds: 100%[=========================] Time: 0:01:17\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬────────────────────────\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├────────────────────────────┼─────────────┼───────────┼────────────────────────\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.399       │ predict   │ [0.285, 0.346, 0.384, ⋯\n",
       "│ BrierScore()               │ -0.222      │ predict   │ [-0.162, -0.181, -0.2 ⋯\n",
       "└────────────────────────────┴─────────────┴───────────┴────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e = evaluate!(mach, resampling=CV(nfolds=6, rng=123),\n",
    "              repeats=3,\n",
    "              measures=[cross_entropy, brier_score])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can access the following properties of the output `e` of an\n",
    "evaluation: `measure`, `measurement`, `per_fold` (measurement for\n",
    "each fold) and `per_observation` (measurement per observation, if\n",
    "reported)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finally note that you can restrict the rows of observations from\n",
    "which train and test folds are drawn, by specifying `rows=...`. For\n",
    "example, imagining the last 30% of target observations are `missing`\n",
    "you might have a work-flow like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Creating subsamples from a subset of all rows. \n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/resampling.jl:495\n",
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:19\u001b[39m\n",
      "┌ Info: Training Machine{NeuralNetworkClassifier{Short,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "\u001b[33mOptimising neural net:100%[=========================] Time: 0:00:03\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "train, test = partition(eachindex(y), 0.7)\n",
    "mach = machine(model, X, y)\n",
    "evaluate!(mach, resampling=CV(nfolds=6),\n",
    "          measures=[cross_entropy, brier_score],\n",
    "          rows=train)     # cv estimate, resampling from `train`\n",
    "fit!(mach, rows=train)    # re-train using all of `train` observations\n",
    "predict(mach, rows=test); # and predict missing targets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On learning curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our model is an iterative one, we might want to inspect the\n",
    "out-of-sample performance as a function of the iteration\n",
    "parameter. For this we can use the `learning_curve` function (which,\n",
    "incidentally can be applied to any model hyper-parameter). This\n",
    "starts by defining a one-dimensional range object for the parameter\n",
    "(more on this when we discuss tuning in Part 4):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NumericRange(1 ≤ epochs ≤ 50; origin=25.5, unit=24.5) on log scale"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = range(model, :epochs, lower=1, upper=50, scale=:log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 22 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 22 metamodels: 100%[=========================] Time: 0:00:06\u001b[39m\n"
     ]
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      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "curve = learning_curve(mach,\n",
    "                       range=r,\n",
    "                       resampling=Holdout(fraction_train=0.7), # (default)\n",
    "                       measure=cross_entropy)\n",
    "\n",
    "using Plots\n",
    "gr(size=(490,300))\n",
    "plt=plot(curve.parameter_values, curve.measurements)\n",
    "xlabel!(plt, \"epochs\")\n",
    "ylabel!(plt, \"cross entropy on holdout set\")\n",
    "savefig(\"learning_curve.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will return to learning curves when we look at tuning in Part 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resources for Part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the MLJ manual:\n",
    "    - [Getting Started](https://alan-turing-institute.github.io/MLJ.jl/dev/getting_started/)\n",
    "    - [Model Search](https://alan-turing-institute.github.io/MLJ.jl/dev/model_search/)\n",
    "    - [Evaluating Performance](https://alan-turing-institute.github.io/MLJ.jl/dev/evaluating_model_performance/) (using `evaluate!`)\n",
    "    - [Learning Curves](https://alan-turing-institute.github.io/MLJ.jl/dev/learning_curves/)\n",
    "    - [Performance Measures](https://alan-turing-institute.github.io/MLJ.jl/dev/performance_measures/) (loss functions, scores, etc)\n",
    "- From Data Science Tutorials:\n",
    "    - [Choosing and evaluating a model](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/choosing-a-model/)\n",
    "    - [Fit, predict, transform](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/fit-and-predict/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises for Part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Identify all supervised MLJ models that can be applied (without\n",
    "type coercion or one-hot encoding) to a supervised learning problem\n",
    "with input features `X4` and target `y4` defined below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CategoricalValue{String, UInt32} \"small\" (1/3)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import Distributions\n",
    "poisson = Distributions.Poisson\n",
    "\n",
    "age = 18 .+ 60*rand(10);\n",
    "salary = coerce(rand([\"small\", \"big\", \"huge\"], 10), OrderedFactor);\n",
    "levels!(salary, [\"small\", \"big\", \"huge\"]);\n",
    "small = CategoricalValue(\"small\", salary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Int64}:\n",
       " 1\n",
       " 0\n",
       " 3\n",
       " 0\n",
       " 1\n",
       " 2\n",
       " 2\n",
       " 2\n",
       " 3\n",
       " 3"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X4 = DataFrames.DataFrame(age=age, salary=salary)\n",
    "\n",
    "n_devices(salary) = salary > small ? rand(poisson(1.3)) : rand(poisson(2.9))\n",
    "y4 = [n_devices(row.salary) for row in eachrow(X4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) What models can be applied if you coerce the salary to a\n",
    "`Continuous` scitype?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 5 (unpack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After evaluating the following ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬────────────┬────────────┬──────────────────────────────────┐\n",
      "│\u001b[1m a     \u001b[0m│\u001b[1m b          \u001b[0m│\u001b[1m c          \u001b[0m│\u001b[1m d                                \u001b[0m│\n",
      "│\u001b[90m Int64 \u001b[0m│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\u001b[90m CategoricalValue{String, UInt32} \u001b[0m│\n",
      "│\u001b[90m Count \u001b[0m│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\u001b[90m OrderedFactor{2}                 \u001b[0m│\n",
      "├───────┼────────────┼────────────┼──────────────────────────────────┤\n",
      "│ 1     │ 0.78377    │ 0.970767   │ male                             │\n",
      "│ 2     │ 0.133496   │ 0.954838   │ female                           │\n",
      "│ 3     │ 0.505917   │ 0.644019   │ female                           │\n",
      "│ 4     │ 0.383093   │ 0.659102   │ male                             │\n",
      "└───────┴────────────┴────────────┴──────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "data = (a = [1, 2, 3, 4],\n",
    "        b = rand(4),\n",
    "        c = rand(4),\n",
    "        d = coerce([\"male\", \"female\", \"female\", \"male\"], OrderedFactor));\n",
    "pretty(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Tables\n",
    "y, X, w = unpack(data,\n",
    "                 ==(:a),\n",
    "                 name -> elscitype(Tables.getcolumn(data, name)) == Continuous,\n",
    "                 name -> true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...attempt to guess the evaluations of the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────┬────────────┐\n",
      "│\u001b[1m b          \u001b[0m│\u001b[1m c          \u001b[0m│\n",
      "│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\n",
      "│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\n",
      "├────────────┼────────────┤\n",
      "│ 0.78377    │ 0.970767   │\n",
      "│ 0.133496   │ 0.954838   │\n",
      "│ 0.505917   │ 0.644019   │\n",
      "│ 0.383093   │ 0.659102   │\n",
      "└────────────┴────────────┘\n"
     ]
    }
   ],
   "source": [
    "pretty(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element CategoricalArray{String,1,UInt32}:\n",
       " \"male\"\n",
       " \"female\"\n",
       " \"female\"\n",
       " \"male\""
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 6 (first steps in modeling Horse Colic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Suppose we want to use predict the `:outcome` variable in the\n",
    "Horse Colic study introduced in Part 1, based on the remaining\n",
    "variables that are `Continuous` (one-hot encoding categorical\n",
    "variables is discussed later in Part 3) *while ignoring the others*.\n",
    "Extract from the `horse` data set (defined in Part 1) appropriate\n",
    "input features `X` and target variable `y`. (Do not, however,\n",
    "randomize the observations.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Create a 70:30 `train`/`test` split of the data and train a\n",
    "`LogisticClassifier` model, from the `MLJLinearModels` package, on\n",
    "the `train` rows. Use `lambda=100` and default values for the\n",
    "other hyper-parameters. (Although one would normally standardize\n",
    "(whiten) the continuous features for this model, do not do so here.)\n",
    "After training:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (i) Recalling that a logistic classifier (aka logistic regressor) is\n",
    "  a linear-based model learning a *vector* of coefficients for each\n",
    "  feature (one coefficient for each target class), use the\n",
    "  `fitted_params` method to find this vector of coefficients in the\n",
    "  case of the `:pulse` feature. (You can convert a vector of pairs `v =\n",
    "  [x1 => y1, x2 => y2, ...]` into a dictionary with `Dict(v)`.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (ii) Evaluate the `cross_entropy` performance on the `test`\n",
    "  observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- &star;(iii) In how many `test` observations does the predicted\n",
    "  probability of the observed class exceed 50%?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (iv) Find the `misclassification_rate` in the `test`\n",
    "  set. (*Hint.* As this measure is deterministic, you will either\n",
    "  need to broadcast `mode` or use `predict_mode` instead of\n",
    "  `predict`.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) Instead use a `RandomForestClassifier` model from the\n",
    "    `DecisionTree` package and:\n",
    "\n",
    "- (i) Generate an appropriate learning curve to convince yourself\n",
    "  that out-of-sample estimates of the `cross_entropy` loss do not\n",
    "  substantially improve for `n_trees > 50`. Use default values for\n",
    "  all other hyper-parameters, and feel free to use all available\n",
    "  data to generate the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (ii) Fix `n_trees=90` and use `evaluate!` to obtain a 9-fold\n",
    "  cross-validation estimate of the `cross_entropy`, restricting\n",
    "  sub-sampling to the `train` observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (iii) Now use *all* available data but set\n",
    "  `resampling=Holdout(fraction_train=0.7)` to obtain a score you can\n",
    "  compare with the `KNNClassifier` in part (b)(iii). Which model is\n",
    "  better?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part-3-transformers-and-pipelines'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3 - Transformers and Pipelines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsupervised models, which receive no target `y` during training,\n",
    "always have a `transform` operation. They sometimes also support an\n",
    "`inverse_transform` operation, with obvious meaning, and sometimes\n",
    "support a `predict` operation (see the clustering example discussed\n",
    "[here](https://alan-turing-institute.github.io/MLJ.jl/dev/transformers/#Transformers-that-also-predict-1)).\n",
    "Otherwise, they are handled much like supervised models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a simple standardization example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean(x) = 0.5163104944541289\n",
      "std(x) = 0.2879206968878454\n"
     ]
    }
   ],
   "source": [
    "x = rand(100);\n",
    "@show mean(x) std(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{Standardizer,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean(xhat) = -2.559064071760986e-16\n",
      "std(xhat) = 1.0\n"
     ]
    }
   ],
   "source": [
    "model = Standardizer() # a built-in model\n",
    "mach = machine(model, x)\n",
    "fit!(mach)\n",
    "xhat = transform(mach, x);\n",
    "@show mean(xhat) std(xhat);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This particular model has an `inverse_transform`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_transform(mach, xhat) ≈ x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Re-encoding the King County House data as continuous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For further illustrations of transformers, let's re-encode *all* of the\n",
    "King County House input features (see [Ex\n",
    "3](#exercise-3-fixing-scitypes-in-a-table)) into a set of `Continuous`\n",
    "features. We do this with the `ContinuousEncoder` model, which, by\n",
    "default, will:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- one-hot encode all `Multiclass` features\n",
    "- coerce all `OrderedFactor` features to `Continuous` ones\n",
    "- coerce all `Count` features to `Continuous` ones (there aren't any)\n",
    "- drop any remaining non-Continuous features (none of these either)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we reload the data and fix the scitypes (Exercise 3):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌───────────────┬───────────────────────────────────┬───────────────────┐\n",
       "│\u001b[22m _.names       \u001b[0m│\u001b[22m _.types                           \u001b[0m│\u001b[22m _.scitypes        \u001b[0m│\n",
       "├───────────────┼───────────────────────────────────┼───────────────────┤\n",
       "│ price         │ Float64                           │ Continuous        │\n",
       "│ bedrooms      │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{13} │\n",
       "│ bathrooms     │ CategoricalValue{Float64, UInt32} │ OrderedFactor{30} │\n",
       "│ sqft_living   │ Float64                           │ Continuous        │\n",
       "│ sqft_lot      │ Float64                           │ Continuous        │\n",
       "│ floors        │ CategoricalValue{Float64, UInt32} │ OrderedFactor{6}  │\n",
       "│ waterfront    │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{2}  │\n",
       "│ view          │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ condition     │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ grade         │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{12} │\n",
       "│ sqft_above    │ Float64                           │ Continuous        │\n",
       "│ sqft_basement │ Float64                           │ Continuous        │\n",
       "│ yr_built      │ Float64                           │ Continuous        │\n",
       "│ zipcode       │ CategoricalValue{Int64, UInt32}   │ Multiclass{70}    │\n",
       "│ lat           │ Float64                           │ Continuous        │\n",
       "│ long          │ Float64                           │ Continuous        │\n",
       "│ sqft_living15 │ Float64                           │ Continuous        │\n",
       "│ sqft_lot15    │ Float64                           │ Continuous        │\n",
       "│ is_renovated  │ CategoricalValue{Bool, UInt32}    │ OrderedFactor{2}  │\n",
       "└───────────────┴───────────────────────────────────┴───────────────────┘\n",
       "_.nrows = 21613\n"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = CSV.File(joinpath(DIR, \"data\", \"house.csv\"));\n",
    "house = DataFrames.DataFrame(file);\n",
    "coerce!(house, autotype(file));\n",
    "coerce!(house, Count => Continuous, :zipcode => Multiclass);\n",
    "schema(house)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = unpack(house, ==(:price), name -> true, rng=123);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instantiate the unsupervised model (transformer):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ContinuousEncoder(\n",
       "    drop_last = false,\n",
       "    one_hot_ordered_factors = false)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encoder = ContinuousEncoder() # a built-in model; no need to @load it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bind the model to the data and fit!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ContinuousEncoder,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    }
   ],
   "source": [
    "mach = machine(encoder, X) |> fit!;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transform and inspect the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌────────────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names        \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├────────────────┼─────────┼────────────┤\n",
       "│ bedrooms       │ Float64 │ Continuous │\n",
       "│ bathrooms      │ Float64 │ Continuous │\n",
       "│ sqft_living    │ Float64 │ Continuous │\n",
       "│ sqft_lot       │ Float64 │ Continuous │\n",
       "│ floors         │ Float64 │ Continuous │\n",
       "│ waterfront     │ Float64 │ Continuous │\n",
       "│ view           │ Float64 │ Continuous │\n",
       "│ condition      │ Float64 │ Continuous │\n",
       "│ grade          │ Float64 │ Continuous │\n",
       "│ sqft_above     │ Float64 │ Continuous │\n",
       "│ sqft_basement  │ Float64 │ Continuous │\n",
       "│ yr_built       │ Float64 │ Continuous │\n",
       "│ zipcode__98001 │ Float64 │ Continuous │\n",
       "│ zipcode__98002 │ Float64 │ Continuous │\n",
       "│ zipcode__98003 │ Float64 │ Continuous │\n",
       "│ zipcode__98004 │ Float64 │ Continuous │\n",
       "│ zipcode__98005 │ Float64 │ Continuous │\n",
       "│ zipcode__98006 │ Float64 │ Continuous │\n",
       "│ zipcode__98007 │ Float64 │ Continuous │\n",
       "│ zipcode__98008 │ Float64 │ Continuous │\n",
       "│ zipcode__98010 │ Float64 │ Continuous │\n",
       "│ zipcode__98011 │ Float64 │ Continuous │\n",
       "│       ⋮        │    ⋮    │     ⋮      │\n",
       "└────────────────┴─────────┴────────────┘\n",
       "\u001b[36m                          65 rows omitted\u001b[0m\n",
       "_.nrows = 21613\n"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xcont = transform(mach, X);\n",
    "schema(Xcont)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More transformers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how to list all of MLJ's unsupervised models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "57-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = ABODDetector, package_name = OutlierDetectionNeighbors, ... )\n",
       " (name = ABODDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = AEDetector, package_name = OutlierDetectionNetworks, ... )\n",
       " (name = AffinityPropagation, package_name = ScikitLearn, ... )\n",
       " (name = AgglomerativeClustering, package_name = ScikitLearn, ... )\n",
       " (name = Birch, package_name = ScikitLearn, ... )\n",
       " (name = CBLOFDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = COFDetector, package_name = OutlierDetectionNeighbors, ... )\n",
       " (name = COFDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = COPODDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = ContinuousEncoder, package_name = MLJModels, ... )\n",
       " (name = DBSCAN, package_name = ScikitLearn, ... )\n",
       " (name = DNNDetector, package_name = OutlierDetectionNeighbors, ... )\n",
       " ⋮\n",
       " (name = PPCA, package_name = MultivariateStats, ... )\n",
       " (name = RODDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = SODDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = SOSDetector, package_name = OutlierDetectionPython, ... )\n",
       " (name = SpectralClustering, package_name = ScikitLearn, ... )\n",
       " (name = Standardizer, package_name = MLJModels, ... )\n",
       " (name = TSVDTransformer, package_name = TSVD, ... )\n",
       " (name = UnivariateBoxCoxTransformer, package_name = MLJModels, ... )\n",
       " (name = UnivariateDiscretizer, package_name = MLJModels, ... )\n",
       " (name = UnivariateFillImputer, package_name = MLJModels, ... )\n",
       " (name = UnivariateStandardizer, package_name = MLJModels, ... )\n",
       " (name = UnivariateTimeTypeToContinuous, package_name = MLJModels, ... )"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models(m->!m.is_supervised)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some commonly used ones are built-in (do not require `@load`ing):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "model type                  | does what?\n",
    "----------------------------|----------------------------------------------\n",
    "ContinuousEncoder | transform input table to a table of `Continuous` features (see above)\n",
    "FeatureSelector | retain or dump selected features\n",
    "FillImputer | impute missing values\n",
    "OneHotEncoder | one-hot encoder `Multiclass` (and optionally `OrderedFactor`) features\n",
    "Standardizer | standardize (whiten) a vector or all `Continuous` features of a table\n",
    "UnivariateBoxCoxTransformer | apply a learned Box-Cox transformation to a vector\n",
    "UnivariateDiscretizer | discretize a `Continuous` vector, and hence render its elscitypw `OrderedFactor`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to \"dynamic\" transformers (ones that learn something\n",
    "from the data and must be `fit!`) users can wrap ordinary functions\n",
    "as transformers, and such *static* transformers can depend on\n",
    "parameters, like the dynamic ones. See\n",
    "[here](https://alan-turing-institute.github.io/MLJ.jl/dev/transformers/#Static-transformers-1)\n",
    "for how to define your own static transformers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pipelines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "87"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(schema(Xcont).names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's suppose that additionally we'd like to reduce the dimension of\n",
    "our data.  A model that will do this is `PCA` from\n",
    "`MultivariateStats`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJMultivariateStatsInterface ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PCA(\n",
       "    maxoutdim = 0,\n",
       "    method = :auto,\n",
       "    pratio = 0.99,\n",
       "    mean = nothing)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA = @load PCA\n",
    "reducer = PCA()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, rather simply repeating the work-flow above, applying the new\n",
    "transformation to `Xcont`, we can combine both the encoding and the\n",
    "dimension-reducing models into a single model, known as a\n",
    "*pipeline*. While MLJ offers a powerful interface for composing\n",
    "models in a variety of ways, we'll stick to these simplest class of\n",
    "composite models for now. The easiest way to construct them is using\n",
    "the `@pipeline` macro:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline292(\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = false),\n",
       "    pca = PCA(\n",
       "            maxoutdim = 0,\n",
       "            method = :auto,\n",
       "            pratio = 0.99,\n",
       "            mean = nothing))"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = @pipeline encoder reducer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that `pipe` is an *instance* of an automatically generated\n",
    "type (called `Pipeline<some digits>`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The new model behaves like any other transformer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{Pipeline292,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{ContinuousEncoder,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{PCA,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "┌─────────┬─────────┬────────────┐\n",
       "│\u001b[22m _.names \u001b[0m│\u001b[22m _.types \u001b[0m│\u001b[22m _.scitypes \u001b[0m│\n",
       "├─────────┼─────────┼────────────┤\n",
       "│ x1      │ Float64 │ Continuous │\n",
       "│ x2      │ Float64 │ Continuous │\n",
       "└─────────┴─────────┴────────────┘\n",
       "_.nrows = 21613\n"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach = machine(pipe, X)\n",
    "fit!(mach)\n",
    "Xsmall = transform(mach, X)\n",
    "schema(Xsmall)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Want to combine this pre-processing with ridge regression?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJLinearModels ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline300(\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = false),\n",
       "    pca = PCA(\n",
       "            maxoutdim = 0,\n",
       "            method = :auto,\n",
       "            pratio = 0.99,\n",
       "            mean = nothing),\n",
       "    ridge_regressor = RidgeRegressor(\n",
       "            lambda = 1.0,\n",
       "            fit_intercept = true,\n",
       "            penalize_intercept = false,\n",
       "            solver = nothing))"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RidgeRegressor = @load RidgeRegressor pkg=MLJLinearModels\n",
    "rgs = RidgeRegressor()\n",
    "pipe2 = @pipeline encoder reducer rgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now our pipeline is a supervised model, instead of a transformer,\n",
    "whose performance we can evaluate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬────────────┐\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold   \u001b[0m│\n",
       "├─────────────────────┼─────────────┼───────────┼────────────┤\n",
       "│ MeanAbsoluteError() │ 234000.0    │ predict   │ [234000.0] │\n",
       "└─────────────────────┴─────────────┴───────────┴────────────┘\n"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach = machine(pipe2, X, y)\n",
    "evaluate!(mach, measure=mae, resampling=Holdout()) # CV(nfolds=6) is default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training of composite models is \"smart\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now notice what happens if we train on all the data, then change a\n",
    "regressor hyper-parameter and retrain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{Pipeline300,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{ContinuousEncoder,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{PCA,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{RidgeRegressor,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{Pipeline300,…} trained 2 times; caches data\n",
       "  args: \n",
       "    1:\tSource @901 ⏎ `Table{Union{AbstractVector{Continuous}, AbstractVector{Multiclass{70}}, AbstractVector{OrderedFactor{6}}, AbstractVector{OrderedFactor{13}}, AbstractVector{OrderedFactor{30}}, AbstractVector{OrderedFactor{5}}, AbstractVector{OrderedFactor{12}}, AbstractVector{OrderedFactor{2}}}}`\n",
       "    2:\tSource @649 ⏎ `AbstractVector{Continuous}`\n"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit!(mach)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{Pipeline300,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Not retraining Machine{ContinuousEncoder,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n",
      "┌ Info: Not retraining Machine{PCA,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n",
      "┌ Info: Updating Machine{RidgeRegressor,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{Pipeline300,…} trained 3 times; caches data\n",
       "  args: \n",
       "    1:\tSource @901 ⏎ `Table{Union{AbstractVector{Continuous}, AbstractVector{Multiclass{70}}, AbstractVector{OrderedFactor{6}}, AbstractVector{OrderedFactor{13}}, AbstractVector{OrderedFactor{30}}, AbstractVector{OrderedFactor{5}}, AbstractVector{OrderedFactor{12}}, AbstractVector{OrderedFactor{2}}}}`\n",
       "    2:\tSource @649 ⏎ `AbstractVector{Continuous}`\n"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe2.ridge_regressor.lambda = 0.1\n",
    "fit!(mach)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second time only the ridge regressor is retrained!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mutate a hyper-parameter of the `PCA` model and every model except\n",
    "the `ContinuousEncoder` (which comes before it will be retrained):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Updating Machine{Pipeline300,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Not retraining Machine{ContinuousEncoder,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n",
      "┌ Info: Updating Machine{PCA,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:404\n",
      "┌ Info: Training Machine{RidgeRegressor,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{Pipeline300,…} trained 4 times; caches data\n",
       "  args: \n",
       "    1:\tSource @901 ⏎ `Table{Union{AbstractVector{Continuous}, AbstractVector{Multiclass{70}}, AbstractVector{OrderedFactor{6}}, AbstractVector{OrderedFactor{13}}, AbstractVector{OrderedFactor{30}}, AbstractVector{OrderedFactor{5}}, AbstractVector{OrderedFactor{12}}, AbstractVector{OrderedFactor{2}}}}`\n",
       "    2:\tSource @649 ⏎ `AbstractVector{Continuous}`\n"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe2.pca.pratio = 0.9999\n",
    "fit!(mach)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspecting composite models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dot syntax used above to change the values of *nested*\n",
    "hyper-parameters is also useful when inspecting the learned\n",
    "parameters and report generated when training a composite model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(coefs = [:x1 => -0.7328956348956878, :x2 => -0.1659056320291739, :x3 => 194.5951589082211, :x4 => 102.71301756136427],\n",
       " intercept = 540085.6428739978,)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_params(mach).ridge_regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(indim = 87,\n",
       " outdim = 4,\n",
       " tprincipalvar = 2.463215246230865e9,\n",
       " tresidualvar = 157533.26199626923,\n",
       " tvar = 2.4633727794928613e9,\n",
       " mean = [4.369869985656781, 8.45912182482765, 2079.8997362698374, 15106.967565816869, 1.988617961412113, 1.0075417572757137, 1.2343034284921113, 3.4094295100171195, 6.6569194466293435, 1788.3906907879516  …  0.011798454633785222, 0.012122333780595013, 0.006292509138018785, 0.012955165872391617, 0.01466709850552908, 47.56005251931713, -122.21389640494186, 1986.552491556008, 12768.455651691113, 1.9577106371165502],\n",
       " principalvars = [2.1770715510450845e9, 2.8418139726430273e8, 1.6850160830643363e6, 277281.8384131831],)"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "report(mach).pca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Incorporating target transformations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, suppose that instead of using the raw `:price` as the\n",
    "training target, we want to use the log-price (a common practice in\n",
    "dealing with house price data). However, suppose that we still want\n",
    "to report final *predictions* on the original linear scale (and use\n",
    "these for evaluation purposes). Then we supply appropriate functions\n",
    "to key-word arguments `target` and `inverse`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we'll overload `log` and `exp` for broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "Base.log(v::AbstractArray) = log.(v)\n",
    "Base.exp(v::AbstractArray) = exp.(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for the new pipeline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Treating pipeline as a `Deterministic` predictor.\n",
      "│ To override, specify `prediction_type=...` (options: :deterministic, :probabilistic, :interval). \n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/composition/models/pipelines.jl:372\n",
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:04\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬───────────────────────────────\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                    \u001b[0m ⋯\n",
       "├─────────────────────┼─────────────┼───────────┼───────────────────────────────\n",
       "│ MeanAbsoluteError() │ 162000.0    │ predict   │ [160000.0, 161000.0, 164000. ⋯\n",
       "└─────────────────────┴─────────────┴───────────┴───────────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe3 = @pipeline encoder reducer rgs target=log inverse=exp\n",
    "mach = machine(pipe3, X, y)\n",
    "evaluate!(mach, measure=mae)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MLJ will also allow you to insert *learned* target\n",
    "transformations. For example, we might want to apply\n",
    "`Standardizer()` to the target, to standardize it, or\n",
    "`UnivariateBoxCoxTransformer()` to make it look Gaussian. Then\n",
    "instead of specifying a *function* for `target`, we specify a\n",
    "unsupervised *model* (or model type). One does not specify `inverse`\n",
    "because only models implementing `inverse_transform` are\n",
    "allowed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see which of these two options results in a better outcome:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Treating pipeline as a `Deterministic` predictor.\n",
      "│ To override, specify `prediction_type=...` (options: :deterministic, :probabilistic, :interval). \n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/composition/models/pipelines.jl:372\n",
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:19\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬───────────────────────────────\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                    \u001b[0m ⋯\n",
       "├─────────────────────┼─────────────┼───────────┼───────────────────────────────\n",
       "│ MeanAbsoluteError() │ 479000.0    │ predict   │ [168000.0, 172000.0, 170000. ⋯\n",
       "└─────────────────────┴─────────────┴───────────┴───────────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "box = UnivariateBoxCoxTransformer(n=20)\n",
    "stand = Standardizer()\n",
    "\n",
    "pipe4 = @pipeline encoder reducer rgs target=box\n",
    "mach = machine(pipe4, X, y)\n",
    "evaluate!(mach, measure=mae)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:03\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬───────────────────────────────\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                    \u001b[0m ⋯\n",
       "├─────────────────────┼─────────────┼───────────┼───────────────────────────────\n",
       "│ MeanAbsoluteError() │ 172000.0    │ predict   │ [173000.0, 171000.0, 172000. ⋯\n",
       "└─────────────────────┴─────────────┴───────────┴───────────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe4.target = stand\n",
    "evaluate!(mach, measure=mae)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resources for Part 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the MLJ manual:\n",
    "    - [Transformers and other unsupervised models](https://alan-turing-institute.github.io/MLJ.jl/dev/transformers/)\n",
    "    - [Linear pipelines](https://alan-turing-institute.github.io/MLJ.jl/dev/linear_pipelines/#Linear-Pipelines)\n",
    "- From Data Science Tutorials:\n",
    "    - [Composing models](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/composing-models/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises for Part 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider again the Horse Colic classification problem considered in\n",
    "Exercise 6, but with all features, `Finite` and `Infinite`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌─────────────────────────┬─────────────────────────────────┬───────────────────\n",
       "│\u001b[22m _.names                 \u001b[0m│\u001b[22m _.types                         \u001b[0m│\u001b[22m _.scitypes      \u001b[0m ⋯\n",
       "├─────────────────────────┼─────────────────────────────────┼───────────────────\n",
       "│ surgery                 │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "│ age                     │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "│ rectal_temperature      │ Float64                         │ Continuous       ⋯\n",
       "│ pulse                   │ Float64                         │ Continuous       ⋯\n",
       "│ respiratory_rate        │ Float64                         │ Continuous       ⋯\n",
       "│ temperature_extremities │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ mucous_membranes        │ CategoricalValue{Int64, UInt32} │ Multiclass{6}    ⋯\n",
       "│ capillary_refill_time   │ CategoricalValue{Int64, UInt32} │ Multiclass{3}    ⋯\n",
       "│ pain                    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{5} ⋯\n",
       "│ peristalsis             │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ abdominal_distension    │ CategoricalValue{Int64, UInt32} │ OrderedFactor{4} ⋯\n",
       "│ packed_cell_volume      │ Float64                         │ Continuous       ⋯\n",
       "│ total_protein           │ Float64                         │ Continuous       ⋯\n",
       "│ surgical_lesion         │ CategoricalValue{Int64, UInt32} │ OrderedFactor{2} ⋯\n",
       "│ cp_data                 │ CategoricalValue{Int64, UInt32} │ Multiclass{2}    ⋯\n",
       "└─────────────────────────┴─────────────────────────────────┴───────────────────\n",
       "_.nrows = 366\n"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = unpack(horse, ==(:outcome), name -> true);\n",
    "schema(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Define a pipeline that:\n",
    "- uses `Standardizer` to ensure that features that are already\n",
    "  continuous are centered at zero and have unit variance\n",
    "- re-encodes the full set of features as `Continuous`, using\n",
    "  `ContinuousEncoder`\n",
    "- uses the `KMeans` clustering model from `Clustering.jl`\n",
    "  to reduce the dimension of the feature space to `k=10`.\n",
    "- trains a `EvoTreeClassifier` (a gradient tree boosting\n",
    "  algorithm in `EvoTrees.jl`) on the reduced data, using\n",
    "  `nrounds=50` and default values for the other\n",
    "   hyper-parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Evaluate the pipeline on all data, using 6-fold cross-validation\n",
    "and `cross_entropy` loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&star;(c) Plot a learning curve which examines the effect on this loss\n",
    "as the tree booster parameter `max_depth` varies from 2 to 10."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part-4-tuning-hyper-parameters'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4 - Tuning Hyper-parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive tuning of a single parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most naive way to tune a single hyper-parameter is to use\n",
    "`learning_curve`, which we already saw in Part 2. Let's see this in\n",
    "the Horse Colic classification problem, in a case where the parameter\n",
    "to be tuned is *nested* (because the model is a pipeline):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJLinearModels ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Machine{Pipeline330,…} trained 0 times; caches data\n",
       "  args: \n",
       "    1:\tSource @064 ⏎ `Table{Union{AbstractVector{Continuous}, AbstractVector{Multiclass{2}}, AbstractVector{Multiclass{6}}, AbstractVector{Multiclass{3}}, AbstractVector{OrderedFactor{2}}, AbstractVector{OrderedFactor{4}}, AbstractVector{OrderedFactor{5}}}}`\n",
       "    2:\tSource @784 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = unpack(horse, ==(:outcome), name -> true);\n",
    "\n",
    "LogisticClassifier = @load LogisticClassifier pkg=MLJLinearModels\n",
    "model = @pipeline Standardizer ContinuousEncoder LogisticClassifier\n",
    "mach = machine(model, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NumericRange(0.01 ≤ logistic_classifier.lambda ≤ 100.0; origin=50.005, unit=49.995) on log10 scale"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = range(model, :(logistic_classifier.lambda), lower = 1e-2, upper=100, scale=:log10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you're curious, you can see what `lambda` values this range will\n",
    "generate for a given resolution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Vector{Float64}:\n",
       "   0.01\n",
       "   0.1\n",
       "   1.0\n",
       "  10.0\n",
       " 100.0"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterator(r, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 30 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 30 metamodels: 100%[=========================] Time: 0:00:27\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5.736152510448679"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, _, lambdas, losses = learning_curve(mach,\n",
    "                                       range=r,\n",
    "                                       resampling=CV(nfolds=6),\n",
    "                                       resolution=30, # default\n",
    "                                       measure=cross_entropy)\n",
    "plt=plot(lambdas, losses, xscale=:log10)\n",
    "xlabel!(plt, \"lambda\")\n",
    "ylabel!(plt, \"cross entropy using 6-fold CV\")\n",
    "savefig(\"learning_curve2.png\")\n",
    "plt\n",
    "\n",
    "\n",
    "best_lambda = lambdas[argmin(losses)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Self tuning models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more sophisticated way to view hyper-parameter tuning (inspired by\n",
    "MLR) is as a model *wrapper*. The wrapped model is a new model in\n",
    "its own right and when you fit it, it tunes specified\n",
    "hyper-parameters of the model being wrapped, before training on all\n",
    "supplied data. Calling `predict` on the wrapped model is like\n",
    "calling `predict` on the original model, but with the\n",
    "hyper-parameters already optimized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, we can think of the wrapped model as a \"self-tuning\"\n",
    "version of the original."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now create a self-tuning version of the pipeline above, adding a\n",
    "parameter from the `ContinuousEncoder` to the parameters we want\n",
    "optimized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's choose a tuning strategy (from [these\n",
    "options](https://github.com/juliaai/MLJTuning.jl#what-is-provided-here)). MLJ\n",
    "supports ordinary `Grid` search (query `?Grid` for\n",
    "details). However, as the utility of `Grid` search is limited to a\n",
    "small number of parameters, and as `Grid` searches are demonstrated\n",
    "elsewhere (see the [resources below](#resources-for-part-4)) we'll\n",
    "demonstrate `RandomSearch` here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomSearch(\n",
       "    bounded = Distributions.Uniform,\n",
       "    positive_unbounded = Distributions.Gamma,\n",
       "    other = Distributions.Normal,\n",
       "    rng = MersenneTwister(123))"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuning = RandomSearch(rng=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this strategy each parameter is sampled according to a\n",
    "pre-specified prior distribution that is fit to the one-dimensional\n",
    "range object constructed using `range` as before. While one has a\n",
    "lot of control over the specification of the priors (run\n",
    "`?RandomSearch` for details) we'll let the algorithm generate these\n",
    "priors automatically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unbounded ranges and sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In MLJ a range does not have to be bounded. In a `RandomSearch` a\n",
    "positive unbounded range is sampled using a `Gamma` distribution, by\n",
    "default:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NumericRange(0.0 ≤ logistic_classifier.lambda ≤ Inf; origin=6.0, unit=5.0) on log10 scale"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = range(model,\n",
    "          :(logistic_classifier.lambda),\n",
    "          lower=0,\n",
    "          origin=6,\n",
    "          unit=5,\n",
    "          scale=:log10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `scale` in a range makes no in a `RandomSearch` (unless it is a\n",
    "function) but this will effect later plots but it does effect the\n",
    "later plots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what sampling using a Gamma distribution is going to mean\n",
    "for this range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import Distributions\n",
    "sampler_r = sampler(r, Distributions.Gamma)\n",
    "plt = histogram(rand(sampler_r, 10000), nbins=50)\n",
    "savefig(\"gamma_sampler.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](gamma_sampler.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second parameter that we'll add to this is *nominal* (finite) and, by\n",
    "default, will be sampled uniformly. Since it is nominal, we specify\n",
    "`values` instead of `upper` and `lower` bounds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NominalRange(continuous_encoder.one_hot_ordered_factors = true, false)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s  = range(model, :(continuous_encoder.one_hot_ordered_factors),\n",
    "           values = [true, false])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The tuning wrapper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for the wrapper, which is an instance of `TunedModel`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ProbabilisticTunedModel(\n",
       "    model = Pipeline330(\n",
       "            standardizer = Standardizer,\n",
       "            continuous_encoder = ContinuousEncoder,\n",
       "            logistic_classifier = LogisticClassifier),\n",
       "    tuning = RandomSearch(\n",
       "            bounded = Distributions.Uniform,\n",
       "            positive_unbounded = Distributions.Gamma,\n",
       "            other = Distributions.Normal,\n",
       "            rng = MersenneTwister(123)),\n",
       "    resampling = CV(\n",
       "            nfolds = 6,\n",
       "            shuffle = false,\n",
       "            rng = Random._GLOBAL_RNG()),\n",
       "    measure = LogLoss(tol = 2.220446049250313e-16),\n",
       "    weights = nothing,\n",
       "    operation = nothing,\n",
       "    range = MLJBase.ParamRange[NumericRange(0.0 ≤ logistic_classifier.lambda ≤ Inf; origin=6.0, unit=5.0) on log10 scale, NominalRange(continuous_encoder.one_hot_ordered_factors = true, false)],\n",
       "    selection_heuristic = MLJTuning.NaiveSelection(nothing),\n",
       "    train_best = true,\n",
       "    repeats = 1,\n",
       "    n = 15,\n",
       "    acceleration = CPU1{Nothing}(nothing),\n",
       "    acceleration_resampling = CPU1{Nothing}(nothing),\n",
       "    check_measure = true,\n",
       "    cache = true)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_model = TunedModel(model=model,\n",
    "                         ranges=[r, s],\n",
    "                         resampling=CV(nfolds=6),\n",
    "                         measures=cross_entropy,\n",
    "                         tuning=tuning,\n",
    "                         n=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the `fit!/predict` work-flow to `tuned_model` just as\n",
    "for any other model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{RandomSearch,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 15 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 15 metamodels: 100%[=========================] Time: 0:00:03\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3-element MLJBase.UnivariateFiniteVector{Multiclass{3}, Int64, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.631, 2=>0.22, 3=>0.149)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.844, 2=>0.00889, 3=>0.147)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.967, 2=>0.0128, 3=>0.0199)"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_mach = machine(tuned_model, X, y);\n",
    "fit!(tuned_mach);\n",
    "predict(tuned_mach, rows=1:3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The outcomes of the tuning can be inspected from a detailed\n",
    "report. For example, we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline330(\n",
       "    standardizer = Standardizer(\n",
       "            features = Symbol[],\n",
       "            ignore = false,\n",
       "            ordered_factor = false,\n",
       "            count = false),\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = true),\n",
       "    logistic_classifier = LogisticClassifier(\n",
       "            lambda = 5.100906526305173,\n",
       "            gamma = 0.0,\n",
       "            penalty = :l2,\n",
       "            fit_intercept = true,\n",
       "            penalize_intercept = false,\n",
       "            solver = nothing))"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rep = report(tuned_mach);\n",
    "rep.best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, sampling of a bounded range is uniform. Lets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the special case of two-parameters, you can also plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt = plot(tuned_mach)\n",
    "savefig(\"tuning.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's compare cross-validation estimate of the performance\n",
    "of the self-tuning model with that of the original model (an example\n",
    "of [*nested\n",
    "resampling*]((https://mlr.mlr-org.com/articles/tutorial/nested_resampling.html)\n",
    "here):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 3 folds: 100%[=========================] Time: 0:00:00\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬────────────────────────\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├────────────────────────────┼─────────────┼───────────┼────────────────────────\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.736       │ predict   │ [0.759, 0.707, 0.741] ⋯\n",
       "└────────────────────────────┴─────────────┴───────────┴────────────────────────\n"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "err = evaluate!(mach, resampling=CV(nfolds=3), measure=cross_entropy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 3 folds: 100%[=========================] Time: 0:00:04\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬────────────────────────\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├────────────────────────────┼─────────────┼───────────┼────────────────────────\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.705       │ predict   │ [0.717, 0.701, 0.697] ⋯\n",
       "└────────────────────────────┴─────────────┴───────────┴────────────────────────\n"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_err = evaluate!(tuned_mach, resampling=CV(nfolds=3), measure=cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='resources-for-part-4'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resources for Part 4\n",
    "\n",
    "- From the MLJ manual:\n",
    "   - [Learning Curves](https://alan-turing-institute.github.io/MLJ.jl/dev/learning_curves/)\n",
    "   - [Tuning Models](https://alan-turing-institute.github.io/MLJ.jl/dev/tuning_models/)\n",
    "- The [MLJTuning repo](https://github.com/juliaai/MLJTuning.jl#who-is-this-repo-for) - mostly for developers\n",
    "\n",
    "- From Data Science Tutorials:\n",
    "    - [Tuning a model](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/model-tuning/)\n",
    "    - [Crabs with XGBoost](https://juliaai.github.io/DataScienceTutorials.jl/end-to-end/crabs-xgb/) `Grid` tuning in stages for a tree-boosting model with many parameters\n",
    "    - [Boston with LightGBM](https://juliaai.github.io/DataScienceTutorials.jl/end-to-end/boston-lgbm/) -  `Grid` tuning for another popular tree-booster\n",
    "    - [Boston with Flux](https://juliaai.github.io/DataScienceTutorials.jl/end-to-end/boston-flux/) - optimizing batch size in a simple neural network regressor\n",
    "- [UCI Horse Colic Data Set](http://archive.ics.uci.edu/ml/datasets/Horse+Colic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises for Part 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This exercise continues our analysis of the King County House price\n",
    "prediction problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = unpack(house, ==(:price), name -> true, rng=123);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your task will be to tune the following pipeline regression model,\n",
    "which includes a gradient tree boosting component:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import EvoTrees ✔"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline345(\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = false),\n",
       "    evo_tree_regressor = EvoTreeRegressor(\n",
       "            loss = EvoTrees.Linear(),\n",
       "            nrounds = 70,\n",
       "            λ = 0.0,\n",
       "            γ = 0.0,\n",
       "            η = 0.1,\n",
       "            max_depth = 5,\n",
       "            min_weight = 1.0,\n",
       "            rowsample = 1.0,\n",
       "            colsample = 1.0,\n",
       "            nbins = 64,\n",
       "            α = 0.5,\n",
       "            metric = :mse,\n",
       "            rng = MersenneTwister(123),\n",
       "            device = \"cpu\"))"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvoTreeRegressor = @load EvoTreeRegressor\n",
    "tree_booster = EvoTreeRegressor(nrounds = 70)\n",
    "model = @pipeline ContinuousEncoder tree_booster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Construct a bounded range `r1` for the `evo_tree_booster`\n",
    "parameter `max_depth`, varying between 1 and 12."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\star&(b) For the `nbins` parameter of the `EvoTreeRegressor`, define the range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "transformed NumericRange(2.5 ≤ evo_tree_regressor.nbins ≤ 7.5; origin=5.0, unit=2.5)"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = range(model,\n",
    "           :(evo_tree_regressor.nbins),\n",
    "           lower = 2.5,\n",
    "           upper= 7.5, scale=x->2^round(Int, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that in this case we've specified a *function* instead of a\n",
    "canned scale, like `:log10`. In this case the `scale` function is\n",
    "applied after sampling (uniformly) between the limits of `lower` and\n",
    "`upper`. Perhaps you can guess the outputs of the following lines of\n",
    "code?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_sampler = sampler(r2, Distributions.Uniform)\n",
    "samples = rand(r2_sampler, 1000);\n",
    "plt = histogram(samples, nbins=50)\n",
    "savefig(\"uniform_sampler.png\")\n",
    "\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](uniform_sampler.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Vector{Int64}:\n",
       "   8\n",
       "  16\n",
       "  32\n",
       "  64\n",
       " 128"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(unique(samples))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) Optimize `model` over these the parameter ranges `r1` and `r2`\n",
    "using a random search with uniform priors (the default). Use\n",
    "`Holdout()` resampling, and implement your search by first\n",
    "constructing a \"self-tuning\" wrap of `model`, as described\n",
    "above. Make `mae` (mean absolute error) the loss function that you\n",
    "optimize, and search over a total of 40 combinations of\n",
    "hyper-parameters.  If you have time, plot the results of your\n",
    "search. Feel free to use all available data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(d) Evaluate the best model found in the search using 3-fold\n",
    "cross-validation and compare with that of the self-tuning model\n",
    "(which is different!). Setting data hygiene concerns aside, feel\n",
    "free to use all available data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part-5-advanced-model-composition'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 5 - Advanced Model Composition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Goals:**\n",
    "> 1. Learn how to build a prototypes of a composite model, called a *learning network*\n",
    "> 2. Learn how to use the `@from_network` macro to export a learning network as a new stand-alone model type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While `@pipeline` is great for composing models in an unbranching\n",
    "sequence, for more complicated model composition you'll want to use\n",
    "MLJ's generic model composition syntax. There are two main steps:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Prototype** the composite model by building a *learning\n",
    "  network*, which can be tested on some (dummy) data as you build\n",
    "  it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Export** the learning network as a new stand-alone model type."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like pipeline models, instances of the exported model type behave\n",
    "like any other model (and are not bound to any data, until you wrap\n",
    "them in a machine)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building a pipeline using the generic composition syntax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To warm up, we'll do the equivalent of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe = @pipeline Standardizer LogisticClassifier;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using the generic syntax."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's some dummy data we'll be using to test our learning network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────┬────────────┬────────────┐\n",
      "│\u001b[1m x1         \u001b[0m│\u001b[1m x2         \u001b[0m│\u001b[1m x3         \u001b[0m│\n",
      "│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\n",
      "│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\n",
      "├────────────┼────────────┼────────────┤\n",
      "│ -8.66643   │ -1.30544   │ -9.4571    │\n",
      "│ -7.35199   │ -1.80323   │ -9.48707   │\n",
      "│ -4.78595   │ 2.98411    │ -0.815858  │\n",
      "│ -8.57023   │ -3.18263   │ -9.14575   │\n",
      "│ -8.57043   │ -1.87734   │ -9.86286   │\n",
      "└────────────┴────────────┴────────────┘\n"
     ]
    }
   ],
   "source": [
    "X, y = make_blobs(5, 3)\n",
    "pretty(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 0** - Proceed as if you were combining the models \"by hand\",\n",
    "using all the data available for training, transforming and\n",
    "prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{Standardizer,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Training Machine{LogisticClassifier,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5-element MLJBase.UnivariateFiniteVector{Multiclass{3}, Int64, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0831, 2=>0.245, 3=>0.672)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.101, 2=>0.172, 3=>0.726)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.832, 2=>0.0589, 3=>0.109)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0506, 2=>0.172, 3=>0.778)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0676, 2=>0.218, 3=>0.715)"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stand = Standardizer();\n",
    "linear = LogisticClassifier();\n",
    "\n",
    "mach1 = machine(stand, X);\n",
    "fit!(mach1);\n",
    "Xstand = transform(mach1, X);\n",
    "\n",
    "mach2 = machine(linear, Xstand, y);\n",
    "fit!(mach2);\n",
    "yhat = predict(mach2, Xstand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 1** - Edit your code as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- pre-wrap the data in `Source` nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- delete the `fit!` calls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Node{Machine{LogisticClassifier,…}}\n",
       "  args:\n",
       "    1:\tNode{Machine{Standardizer,…}}\n",
       "  formula:\n",
       "    predict(\n",
       "        Machine{LogisticClassifier,…}, \n",
       "        transform(\n",
       "            Machine{Standardizer,…}, \n",
       "            Source @439))"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = source(X)  # or X = source() if not testing\n",
    "y = source(y)  # or y = source()\n",
    "\n",
    "stand = Standardizer();\n",
    "linear = LogisticClassifier();\n",
    "\n",
    "mach1 = machine(stand, X);\n",
    "Xstand = transform(mach1, X);\n",
    "\n",
    "mach2 = machine(linear, Xstand, y);\n",
    "yhat = predict(mach2, Xstand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now `X`, `y`, `Xstand` and `yhat` are *nodes* (\"variables\" or\n",
    "\"dynammic data\") instead of data. All training, predicting and\n",
    "transforming is now executed lazily, whenever we `fit!` one of these\n",
    "nodes. We *call* a node to retrieve the data it represents in the\n",
    "original manual workflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{Standardizer,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────┬────────────┬────────────┐\n",
      "│\u001b[1m x1         \u001b[0m│\u001b[1m x2         \u001b[0m│\u001b[1m x3         \u001b[0m│\n",
      "│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\u001b[90m Float64    \u001b[0m│\n",
      "│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\u001b[90m Continuous \u001b[0m│\n",
      "├────────────┼────────────┼────────────┤\n",
      "│ -0.649707  │ -0.114144  │ -0.438255  │\n",
      "│ 0.142925   │ -0.325739  │ -0.445966  │\n",
      "│ 1.6903     │ 1.7092     │ 1.78502    │\n",
      "│ -0.591698  │ -0.912075  │ -0.35815   │\n",
      "│ -0.591816  │ -0.357242  │ -0.542651  │\n",
      "└────────────┴────────────┴────────────┘\n"
     ]
    }
   ],
   "source": [
    "fit!(Xstand)\n",
    "Xstand() |> pretty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Not retraining Machine{Standardizer,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n",
      "┌ Info: Training Machine{LogisticClassifier,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5-element MLJBase.UnivariateFiniteVector{Multiclass{3}, Int64, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0831, 2=>0.245, 3=>0.672)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.101, 2=>0.172, 3=>0.726)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.832, 2=>0.0589, 3=>0.109)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0506, 2=>0.172, 3=>0.778)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0676, 2=>0.218, 3=>0.715)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit!(yhat);\n",
    "yhat()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The node `yhat` is the \"descendant\" (in an associated DAG we have\n",
    "defined) of a unique source node:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Any}:\n",
       " Source @439 ⏎ `Table{AbstractVector{Continuous}}`\n",
       " Source @857 ⏎ `AbstractVector{Multiclass{3}}`"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sources(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data at the source node is replaced by `Xnew` to obtain a\n",
    "new prediction when we call `yhat` like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element MLJBase.UnivariateFiniteVector{Multiclass{3}, Int64, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.000335, 2=>0.000995, 3=>0.999)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.0928, 2=>0.00217, 3=>0.905)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xnew, _ = make_blobs(2, 3);\n",
    "yhat(Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 2** - Export the learning network as a new stand-alone model type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, somewhat paradoxically, we can wrap the whole network in a\n",
    "special machine - called a *learning network machine* - before have\n",
    "defined the new model type. Indeed doing so is a necessary step in\n",
    "the export process, for this machine will tell the export macro:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- what kind of model the composite will be (`Deterministic`,\n",
    "  `Probabilistic` or `Unsupervised`)a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- which source nodes are input nodes and which are for the target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- which nodes correspond to each operation (`predict`, `transform`,\n",
    "  etc) that we might want to define"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Machine{ProbabilisticSurrogate,…} trained 0 times; does not cache data\n",
       "  args: \n",
       "    1:\tSource @439 ⏎ `Table{AbstractVector{Continuous}}`\n",
       "    2:\tSource @857 ⏎ `AbstractVector{Multiclass{3}}`\n"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "surrogate = Probabilistic()     # a model with no fields!\n",
    "mach = machine(surrogate, X, y; predict=yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although we have no real need to use it, this machine behaves like\n",
    "you'd expect it to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Not retraining Machine{Standardizer,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n",
      "┌ Info: Not retraining Machine{LogisticClassifier,…}. Use `force=true` to force.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:406\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2-element MLJBase.UnivariateFiniteVector{Multiclass{3}, Int64, UInt32, Float64}:\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.108, 2=>0.135, 3=>0.757)\n",
       " UnivariateFinite{Multiclass{3}}(1=>0.324, 2=>0.0784, 3=>0.597)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xnew, _ = make_blobs(2, 3)\n",
    "fit!(mach)\n",
    "predict(mach, Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we create a new model type using a Julia `struct` definition\n",
    "appropriately decorated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "@from_network mach begin\n",
    "    mutable struct YourPipe\n",
    "        standardizer = stand\n",
    "        classifier = linear::Probabilistic\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instantiating and evaluating on some new data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:02\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────────┬─────────────┬──────────────┬────────────────────────\n",
       "│\u001b[22m measure                 \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation    \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├─────────────────────────┼─────────────┼──────────────┼────────────────────────\n",
       "│ MisclassificationRate() │ 0.08        │ predict_mode │ [0.0, 0.04, 0.08, 0.0 ⋯\n",
       "└─────────────────────────┴─────────────┴──────────────┴────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = YourPipe()\n",
    "X, y = @load_iris;   # built-in data set\n",
    "mach = machine(pipe, X, y)\n",
    "evaluate!(mach, measure=misclassification_rate, operation=predict_mode)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A composite model to average two regressor predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following is condensed version of\n",
    "[this](https://github.com/alan-turing-institute/MLJ.jl/blob/master/binder/MLJ_demo.ipynb)\n",
    "tutorial. We will define a composite model that:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- standardizes the input data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- learns and applies a Box-Cox transformation to the target variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- blends the predictions of two supervised learning models - a ridge\n",
    " regressor and a random forest regressor; we'll blend using a simple\n",
    " average (for a more sophisticated stacking example, see\n",
    " [here](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/stacking/))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- applies the *inverse* Box-Cox transformation to this blended prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJDecisionTreeInterface ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLJDecisionTreeInterface.RandomForestRegressor"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RandomForestRegressor = @load RandomForestRegressor pkg=DecisionTree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Input layer**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Source @471 ⏎ `Nothing`"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = source()\n",
    "y = source()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First layer and target transformation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Node{Machine{UnivariateBoxCoxTransformer,…}}\n",
       "  args:\n",
       "    1:\tSource @471\n",
       "  formula:\n",
       "    transform(\n",
       "        Machine{UnivariateBoxCoxTransformer,…}, \n",
       "        Source @471)"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_model = Standardizer()\n",
    "stand = machine(std_model, X)\n",
    "W = MLJ.transform(stand, X)\n",
    "\n",
    "box_model = UnivariateBoxCoxTransformer()\n",
    "box = machine(box_model, y)\n",
    "z = MLJ.transform(box, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Second layer**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Node{Nothing}\n",
       "  args:\n",
       "    1:\tNode{Nothing}\n",
       "    2:\tNode{Nothing}\n",
       "  formula:\n",
       "    +(\n",
       "        #134(\n",
       "            predict(\n",
       "                Machine{RidgeRegressor,…}, \n",
       "                transform(\n",
       "                    Machine{Standardizer,…}, \n",
       "                    Source @346))),\n",
       "        #134(\n",
       "            predict(\n",
       "                Machine{RandomForestRegressor,…}, \n",
       "                transform(\n",
       "                    Machine{Standardizer,…}, \n",
       "                    Source @346))))"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_model = RidgeRegressor(lambda=0.1)\n",
    "ridge = machine(ridge_model, W, z)\n",
    "\n",
    "forest_model = RandomForestRegressor(n_trees=50)\n",
    "forest = machine(forest_model, W, z)\n",
    "\n",
    "ẑ = 0.5*predict(ridge, W) + 0.5*predict(forest, W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Output**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Node{Machine{UnivariateBoxCoxTransformer,…}}\n",
       "  args:\n",
       "    1:\tNode{Nothing}\n",
       "  formula:\n",
       "    inverse_transform(\n",
       "        Machine{UnivariateBoxCoxTransformer,…}, \n",
       "        +(\n",
       "            #134(\n",
       "                predict(\n",
       "                    Machine{RidgeRegressor,…}, \n",
       "                    transform(\n",
       "                        Machine{Standardizer,…}, \n",
       "                        Source @346))),\n",
       "            #134(\n",
       "                predict(\n",
       "                    Machine{RandomForestRegressor,…}, \n",
       "                    transform(\n",
       "                        Machine{Standardizer,…}, \n",
       "                        Source @346)))))"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ŷ = inverse_transform(box, ẑ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the learning network defined, we're ready to export:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "@from_network machine(Deterministic(), X, y, predict=ŷ) begin\n",
    "    mutable struct CompositeModel\n",
    "        rgs1 = ridge_model\n",
    "        rgs2 = forest_model\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's instantiate the new model type and try it out on some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CompositeModel(\n",
       "    rgs1 = RidgeRegressor(\n",
       "            lambda = 0.1,\n",
       "            fit_intercept = true,\n",
       "            penalize_intercept = false,\n",
       "            solver = nothing),\n",
       "    rgs2 = RandomForestRegressor(\n",
       "            max_depth = -1,\n",
       "            min_samples_leaf = 1,\n",
       "            min_samples_split = 2,\n",
       "            min_purity_increase = 0.0,\n",
       "            n_subfeatures = -1,\n",
       "            n_trees = 50,\n",
       "            sampling_fraction = 0.7,\n",
       "            pdf_smoothing = 0.0,\n",
       "            rng = Random._GLOBAL_RNG()))"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composite = CompositeModel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:06\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────┬─────────────┬───────────┬────────────────────────────\n",
       "│\u001b[22m measure                \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                 \u001b[0m ⋯\n",
       "├────────────────────────┼─────────────┼───────────┼────────────────────────────\n",
       "│ RootMeanSquaredError() │ 3.89        │ predict   │ [3.89, 3.93, 2.79, 2.81,  ⋯\n",
       "│ MeanAbsoluteError()    │ 2.46        │ predict   │ [2.59, 2.44, 2.1, 2.16, 2 ⋯\n",
       "└────────────────────────┴─────────────┴───────────┴────────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = @load_boston;\n",
    "mach = machine(composite, X, y);\n",
    "evaluate!(mach,\n",
    "          resampling=CV(nfolds=6, shuffle=true),\n",
    "          measures=[rms, mae])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resources for Part 5\n",
    "\n",
    "- From the MLJ manual:\n",
    "   - [Learning Networks](https://alan-turing-institute.github.io/MLJ.jl/stable/composing_models/#Learning-Networks-1)\n",
    "- From Data Science Tutorials:\n",
    "    - [Learning Networks](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/learning-networks/)\n",
    "    - [Learning Networks 2](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/learning-networks-2/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    - [Stacking](https://juliaai.github.io/DataScienceTutorials.jl/getting-started/stacking/): an advanced example of model composition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    - [Finer Control](https://alan-turing-institute.github.io/MLJ.jl/dev/composing_models/#Method-II:-Finer-control-(advanced)-1):\n",
    "      exporting learning networks without a macro for finer control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='solutions-to-exercises'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions to exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2 solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Trying to coerce from `Union{Missing, String}` to `OrderedFactor`.\n",
      "│ Coerced to `Union{Missing,OrderedFactor}` instead.\n",
      "└ @ ScientificTypes /Users/anthony/.julia/packages/ScientificTypes/z5Vmr/src/convention/coerce.jl:174\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Union{Missing, OrderedFactor{3}}"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quality = coerce(quality, OrderedFactor);\n",
    "levels!(quality, [\"poor\", \"good\", \"excellent\"]);\n",
    "elscitype(quality)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3 solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First pass:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌───────────────┬───────────────────────────────────┬───────────────────┐\n",
       "│\u001b[22m _.names       \u001b[0m│\u001b[22m _.types                           \u001b[0m│\u001b[22m _.scitypes        \u001b[0m│\n",
       "├───────────────┼───────────────────────────────────┼───────────────────┤\n",
       "│ price         │ Float64                           │ Continuous        │\n",
       "│ bedrooms      │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{13} │\n",
       "│ bathrooms     │ CategoricalValue{Float64, UInt32} │ OrderedFactor{30} │\n",
       "│ sqft_living   │ Float64                           │ Continuous        │\n",
       "│ sqft_lot      │ Float64                           │ Continuous        │\n",
       "│ floors        │ CategoricalValue{Float64, UInt32} │ OrderedFactor{6}  │\n",
       "│ waterfront    │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{2}  │\n",
       "│ view          │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ condition     │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ grade         │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{12} │\n",
       "│ sqft_above    │ Float64                           │ Continuous        │\n",
       "│ sqft_basement │ Float64                           │ Continuous        │\n",
       "│ yr_built      │ Float64                           │ Continuous        │\n",
       "│ zipcode       │ CategoricalValue{Int64, UInt32}   │ Multiclass{70}    │\n",
       "│ lat           │ Float64                           │ Continuous        │\n",
       "│ long          │ Float64                           │ Continuous        │\n",
       "│ sqft_living15 │ Float64                           │ Continuous        │\n",
       "│ sqft_lot15    │ Float64                           │ Continuous        │\n",
       "│ is_renovated  │ CategoricalValue{Bool, UInt32}    │ OrderedFactor{2}  │\n",
       "└───────────────┴───────────────────────────────────┴───────────────────┘\n",
       "_.nrows = 21613\n"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(house, autotype(house));\n",
    "schema(house)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the \"sqft\" fields refer to \"square feet\" so are\n",
    "really `Continuous`. We'll regard `:yr_built` (the other `Count`\n",
    "variable above) as `Continuous` as well. So:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "coerce!(house, Count => Continuous);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And `:zipcode` should not be ordered:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "┌───────────────┬───────────────────────────────────┬───────────────────┐\n",
       "│\u001b[22m _.names       \u001b[0m│\u001b[22m _.types                           \u001b[0m│\u001b[22m _.scitypes        \u001b[0m│\n",
       "├───────────────┼───────────────────────────────────┼───────────────────┤\n",
       "│ price         │ Float64                           │ Continuous        │\n",
       "│ bedrooms      │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{13} │\n",
       "│ bathrooms     │ CategoricalValue{Float64, UInt32} │ OrderedFactor{30} │\n",
       "│ sqft_living   │ Float64                           │ Continuous        │\n",
       "│ sqft_lot      │ Float64                           │ Continuous        │\n",
       "│ floors        │ CategoricalValue{Float64, UInt32} │ OrderedFactor{6}  │\n",
       "│ waterfront    │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{2}  │\n",
       "│ view          │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ condition     │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{5}  │\n",
       "│ grade         │ CategoricalValue{Int64, UInt32}   │ OrderedFactor{12} │\n",
       "│ sqft_above    │ Float64                           │ Continuous        │\n",
       "│ sqft_basement │ Float64                           │ Continuous        │\n",
       "│ yr_built      │ Float64                           │ Continuous        │\n",
       "│ zipcode       │ CategoricalValue{Int64, UInt32}   │ Multiclass{70}    │\n",
       "│ lat           │ Float64                           │ Continuous        │\n",
       "│ long          │ Float64                           │ Continuous        │\n",
       "│ sqft_living15 │ Float64                           │ Continuous        │\n",
       "│ sqft_lot15    │ Float64                           │ Continuous        │\n",
       "│ is_renovated  │ CategoricalValue{Bool, UInt32}    │ OrderedFactor{2}  │\n",
       "└───────────────┴───────────────────────────────────┴───────────────────┘\n",
       "_.nrows = 21613\n"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coerce!(house, :zipcode => Multiclass);\n",
    "schema(house)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`:bathrooms` looks like it has a lot of levels, but on further\n",
    "inspection we see why, and `OrderedFactor` remains appropriate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{CategoricalValue{Float64, UInt32}, Int64} with 30 entries:\n",
       "  5.0  => 21\n",
       "  5.25 => 13\n",
       "  1.25 => 9\n",
       "  8.0  => 2\n",
       "  6.75 => 2\n",
       "  1.0  => 3852\n",
       "  5.5  => 10\n",
       "  0.0  => 10\n",
       "  6.0  => 6\n",
       "  6.25 => 2\n",
       "  4.75 => 23\n",
       "  3.25 => 589\n",
       "  3.0  => 753\n",
       "  2.25 => 2047\n",
       "  0.5  => 4\n",
       "  7.5  => 1\n",
       "  5.75 => 4\n",
       "  1.5  => 1446\n",
       "  3.75 => 155\n",
       "  4.0  => 136\n",
       "  4.25 => 79\n",
       "  2.0  => 1930\n",
       "  2.75 => 1185\n",
       "  3.5  => 731\n",
       "  6.5  => 2\n",
       "  ⋮    => ⋮"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import StatsBase.countmap\n",
    "countmap(house.bathrooms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 4 solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are *no* models that apply immediately:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple[]"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models(matching(X4, y4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Vector{NamedTuple{(:name, :package_name, :is_supervised, :abstract_type, :deep_properties, :docstring, :fit_data_scitype, :hyperparameter_ranges, :hyperparameter_types, :hyperparameters, :implemented_methods, :inverse_transform_scitype, :is_pure_julia, :is_wrapper, :iteration_parameter, :load_path, :package_license, :package_url, :package_uuid, :predict_scitype, :prediction_type, :supports_class_weights, :supports_online, :supports_training_losses, :supports_weights, :transform_scitype, :input_scitype, :target_scitype, :output_scitype), T} where T<:Tuple}:\n",
       " (name = ConstantRegressor, package_name = MLJModels, ... )\n",
       " (name = DecisionTreeRegressor, package_name = BetaML, ... )\n",
       " (name = DecisionTreeRegressor, package_name = DecisionTree, ... )\n",
       " (name = DeterministicConstantRegressor, package_name = MLJModels, ... )\n",
       " (name = RandomForestRegressor, package_name = BetaML, ... )\n",
       " (name = RandomForestRegressor, package_name = DecisionTree, ... )"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y4 = coerce(y4, Continuous);\n",
    "models(matching(X4, y4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 6 solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = unpack(horse,\n",
    "              ==(:outcome),\n",
    "              name -> elscitype(Tables.getcolumn(horse, name)) == Continuous);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(b)(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJLinearModels ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n",
      "┌ Info: Training Machine{LogisticClassifier,…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(classes = CategoricalValue{Int64, UInt32}[1, 2, 3],\n",
       " coefs = Pair{Symbol, SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}[:rectal_temperature => [0.061700165029243595, -0.06507181612449195, 0.003371651095248075], :pulse => [-0.009584825604133507, 0.004022558654903623, 0.005562266949230421], :respiratory_rate => [-0.009584825604133507, 0.004022558654903623, 0.005562266949230421], :packed_cell_volume => [-0.04309372172868995, 0.020859863946466082, 0.022233857782222862], :total_protein => [0.02750875240430624, -0.06317268051316188, 0.03566392810885553]],\n",
       " intercept = [0.0008917385182322375, -0.000891738518934035, -4.972412447643922],)"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = (@load LogisticClassifier pkg=MLJLinearModels)();\n",
    "model.lambda = 100\n",
    "mach = machine(model, X, y)\n",
    "fit!(mach, rows=train)\n",
    "fitted_params(mach)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7187276476001894"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs_given_feature = Dict(fitted_params(mach).coefs)\n",
    "coefs_given_feature[:pulse]\n",
    "\n",
    "#6(b)(ii)\n",
    "\n",
    "yhat = predict(mach, rows=test); # or predict(mach, X[test,:])\n",
    "err = cross_entropy(yhat, y[test]) |> mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(b)(iii)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted probabilities of the actual observations in the test\n",
    "are given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = broadcast(pdf, yhat, y[test]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of times this probability exceeds 50% is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n50 = filter(x -> x > 0.5, p) |> length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, as a proportion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666666"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n50/length(test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(b)(iv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28888888888888886"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "misclassification_rate(mode.(yhat), y[test])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(c)(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJDecisionTreeInterface ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n",
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:01\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "NumericRange(10 ≤ n_trees ≤ 70; origin=40.0, unit=30.0) on log10 scale"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = (@load RandomForestClassifier pkg=DecisionTree)()\n",
    "mach = machine(model, X, y)\n",
    "evaluate!(mach, resampling=CV(nfolds=6), measure=cross_entropy)\n",
    "\n",
    "r = range(model, :n_trees, lower=10, upper=70, scale=:log10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since random forests are inherently randomized, we generate multiple\n",
    "curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 29 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 29 metamodels: 100%[=========================] Time: 0:00:01\u001b[39m\n",
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 29 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 29 metamodels: 100%[=========================] Time: 0:00:00\u001b[39m\n",
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 29 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 29 metamodels: 100%[=========================] Time: 0:00:00\u001b[39m\n",
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 29 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 29 metamodels: 100%[=========================] Time: 0:00:00\u001b[39m\n"
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      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt = plot()\n",
    "for i in 1:4\n",
    "    one_curve = learning_curve(mach,\n",
    "                           range=r,\n",
    "                           resampling=Holdout(),\n",
    "                           measure=cross_entropy)\n",
    "    plot!(one_curve.parameter_values, one_curve.measurements)\n",
    "end\n",
    "xlabel!(plt, \"n_trees\")\n",
    "ylabel!(plt, \"cross entropy\")\n",
    "savefig(\"exercise_6ci.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(c)(ii)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Creating subsamples from a subset of all rows. \n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/resampling.jl:495\n",
      "\u001b[33mEvaluating over 9 folds: 100%[=========================] Time: 0:00:00\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "90"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate!(mach, resampling=CV(nfolds=9),\n",
    "                measure=cross_entropy,\n",
    "                rows=train).measurement[1]\n",
    "\n",
    "model.n_trees = 90"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6(c)(iii)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6868562419362649"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "err_forest = evaluate!(mach, resampling=Holdout(),\n",
    "                       measure=cross_entropy).measurement[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJClusteringInterface ✔\n",
      "import EvoTrees ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n",
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline371(\n",
       "    standardizer = Standardizer(\n",
       "            features = Symbol[],\n",
       "            ignore = false,\n",
       "            ordered_factor = false,\n",
       "            count = false),\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = false),\n",
       "    k_means = KMeans(\n",
       "            k = 10,\n",
       "            metric = Distances.SqEuclidean(0.0)),\n",
       "    evo_tree_classifier = EvoTreeClassifier(\n",
       "            loss = EvoTrees.Softmax(),\n",
       "            nrounds = 50,\n",
       "            λ = 0.0,\n",
       "            γ = 0.0,\n",
       "            η = 0.1,\n",
       "            max_depth = 5,\n",
       "            min_weight = 1.0,\n",
       "            rowsample = 1.0,\n",
       "            colsample = 1.0,\n",
       "            nbins = 64,\n",
       "            α = 0.5,\n",
       "            metric = :mlogloss,\n",
       "            rng = MersenneTwister(123),\n",
       "            device = \"cpu\"))"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "KMeans = @load KMeans pkg=Clustering\n",
    "EvoTreeClassifier = @load EvoTreeClassifier\n",
    "pipe = @pipeline(Standardizer,\n",
    "                 ContinuousEncoder,\n",
    "                 KMeans(k=10),\n",
    "                 EvoTreeClassifier(nrounds=50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 6 folds: 100%[=========================] Time: 0:00:28\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌────────────────────────────┬─────────────┬───────────┬────────────────────────\n",
       "│\u001b[22m measure                    \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold             \u001b[0m ⋯\n",
       "├────────────────────────────┼─────────────┼───────────┼────────────────────────\n",
       "│ LogLoss(tol = 2.22045e-16) │ 0.783       │ predict   │ [0.757, 0.862, 0.76,  ⋯\n",
       "└────────────────────────────┴─────────────┴───────────┴────────────────────────\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mach = machine(pipe, X, y)\n",
    "evaluate!(mach, resampling=CV(nfolds=6), measure=cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 10 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 10 metamodels: 100%[=========================] Time: 0:00:13\u001b[39m\n"
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     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = range(pipe, :(evo_tree_classifier.max_depth), lower=1, upper=10)\n",
    "\n",
    "curve = learning_curve(mach,\n",
    "                       range=r,\n",
    "                       resampling=CV(nfolds=6),\n",
    "                       measure=cross_entropy)\n",
    "\n",
    "plt = plot(curve.parameter_values, curve.measurements)\n",
    "xlabel!(plt, \"max_depth\")\n",
    "ylabel!(plt, \"CV estimate of cross entropy\")\n",
    "savefig(\"exercise_7c.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a second curve using a different random seed for the booster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{ProbabilisticTunedModel{Grid,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 10 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 10 metamodels: 100%[=========================] Time: 0:00:13\u001b[39m\n"
     ]
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      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Random\n",
    "pipe.evo_tree_classifier.rng = MersenneTwister(123)\n",
    "curve = learning_curve(mach,\n",
    "                       range=r,\n",
    "                       resampling=CV(nfolds=6),\n",
    "                       measure=cross_entropy)\n",
    "plot!(curve.parameter_values, curve.measurements)\n",
    "savefig(\"exercise_7c_2.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can automatic the production of multiple curves with different\n",
    "seeds in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating Learning curve with 6 rngs: 100%[==================] Time: 0:01:30\u001b[39m\n"
     ]
    },
    {
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      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "curves = learning_curve(mach,\n",
    "                        range=r,\n",
    "                        resampling=CV(nfolds=6),\n",
    "                        measure=cross_entropy,\n",
    "                        rng_name=:(evo_tree_classifier.rng),\n",
    "                        rngs=6) # list of RNGs, or num to auto generate\n",
    "plt = plot(curves.parameter_values, curves.measurements)\n",
    "savefig(\"exercise_7c_3.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have multiple threads available in your julia session, you\n",
    "can add the option `acceleration=CPUThreads()` to speed up this\n",
    "computation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import EvoTrees ✔\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: For silent loading, specify `verbosity=0`. \n",
      "└ @ Main /Users/anthony/.julia/packages/MLJModels/4sRmw/src/loading.jl:168\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline401(\n",
       "    continuous_encoder = ContinuousEncoder(\n",
       "            drop_last = false,\n",
       "            one_hot_ordered_factors = false),\n",
       "    evo_tree_regressor = EvoTreeRegressor(\n",
       "            loss = EvoTrees.Linear(),\n",
       "            nrounds = 70,\n",
       "            λ = 0.0,\n",
       "            γ = 0.0,\n",
       "            η = 0.1,\n",
       "            max_depth = 5,\n",
       "            min_weight = 1.0,\n",
       "            rowsample = 1.0,\n",
       "            colsample = 1.0,\n",
       "            nbins = 64,\n",
       "            α = 0.5,\n",
       "            metric = :mse,\n",
       "            rng = MersenneTwister(123),\n",
       "            device = \"cpu\"))"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = unpack(house, ==(:price), name -> true, rng=123);\n",
    "\n",
    "EvoTreeRegressor = @load EvoTreeRegressor\n",
    "tree_booster = EvoTreeRegressor(nrounds = 70)\n",
    "model = @pipeline ContinuousEncoder tree_booster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NumericRange(1 ≤ evo_tree_regressor.max_depth ≤ 12; origin=6.5, unit=5.5)"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1 = range(model, :(evo_tree_regressor.max_depth), lower=1, upper=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Training Machine{DeterministicTunedModel{RandomSearch,…},…}.\n",
      "└ @ MLJBase /Users/anthony/.julia/packages/MLJBase/HZmTU/src/machines.jl:403\n",
      "┌ Info: Attempting to evaluate 40 models.\n",
      "└ @ MLJTuning /Users/anthony/.julia/packages/MLJTuning/efiDR/src/tuned_models.jl:685\n",
      "\u001b[33mEvaluating over 40 metamodels: 100%[=========================] Time: 0:03:31\u001b[39m\n"
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       "<circle clip-path=\"url(#clip495)\" cx=\"2134.7\" cy=\"1758.83\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "<circle clip-path=\"url(#clip495)\" cx=\"1813.68\" cy=\"1750.81\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "<circle clip-path=\"url(#clip495)\" cx=\"1532.79\" cy=\"1668.29\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "<circle clip-path=\"url(#clip495)\" cx=\"1532.79\" cy=\"1646.65\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "<circle clip-path=\"url(#clip495)\" cx=\"1653.17\" cy=\"1735.21\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "<circle clip-path=\"url(#clip495)\" cx=\"1653.17\" cy=\"1754.86\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"4\"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_model = TunedModel(model=model,\n",
    "                         ranges=[r1, r2],\n",
    "                         resampling=Holdout(),\n",
    "                         measures=mae,\n",
    "                         tuning=RandomSearch(rng=123),\n",
    "                         n=40)\n",
    "\n",
    "tuned_mach = machine(tuned_model, X, y) |> fit!\n",
    "plt = plot(tuned_mach)\n",
    "savefig(\"exercise_8c.png\")\n",
    "plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 3 folds: 100%[=========================] Time: 0:00:50\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬─────────────────────────────┐\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                    \u001b[0m│\n",
       "├─────────────────────┼─────────────┼───────────┼─────────────────────────────┤\n",
       "│ MeanAbsoluteError() │ 68700.0     │ predict   │ [68800.0, 67800.0, 69500.0] │\n",
       "└─────────────────────┴─────────────┴───────────┴─────────────────────────────┘\n"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_model = report(tuned_mach).best_model;\n",
    "best_mach = machine(best_model, X, y);\n",
    "best_err = evaluate!(best_mach, resampling=CV(nfolds=3), measure=mae)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33mEvaluating over 3 folds: 100%[=========================] Time: 0:07:17\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PerformanceEvaluation object with these fields:\n",
       "  measure, measurement, operation, per_fold,\n",
       "  per_observation, fitted_params_per_fold,\n",
       "  report_per_fold, train_test_pairs\n",
       "Extract:\n",
       "┌─────────────────────┬─────────────┬───────────┬─────────────────────────────┐\n",
       "│\u001b[22m measure             \u001b[0m│\u001b[22m measurement \u001b[0m│\u001b[22m operation \u001b[0m│\u001b[22m per_fold                    \u001b[0m│\n",
       "├─────────────────────┼─────────────┼───────────┼─────────────────────────────┤\n",
       "│ MeanAbsoluteError() │ 69900.0     │ predict   │ [71400.0, 67800.0, 70500.0] │\n",
       "└─────────────────────┴─────────────┴───────────┴─────────────────────────────┘\n"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_err = evaluate!(tuned_mach, resampling=CV(nfolds=3), measure=mae)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ]
  }
 ],
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