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David Seiler
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PDF operators for each distribution for which we have a random sampler (plus also the PDF of the Dirichlet). Supports probabilities and log-probabilities, as well as gradients.
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‎src/operator/random/pdf_op.cc

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/*
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* Licensed to the Apache Software Foundation (ASF) under one
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* or more contributor license agreements. See the NOTICE file
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* distributed with this work for additional information
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* regarding copyright ownership. The ASF licenses this file
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* to you under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance
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* with the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing,
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* software distributed under the License is distributed on an
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* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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* KIND, either express or implied. See the License for the
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* specific language governing permissions and limitations
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* under the License.
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*/
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/*!
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* Copyright (c) 2018 by Contributors
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* \file pdf_op.cc
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* \brief CPU-operators for computing the pdf of random distributions.
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*/
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#include "./pdf_op.h"
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namespace mxnet {
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namespace op {
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DMLC_REGISTER_PARAMETER(PdfParam);
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#define MXNET_OPERATOR_REGISTER_PDF(distr, pdffunc, num_parms, \
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parm_name_1, parm_name_2, \
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parm_desc_1, parm_desc_2, \
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description, vectorparms) \
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NNVM_REGISTER_OP(_random_pdf_##distr) \
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.add_alias("random_pdf_" #distr) \
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.describe(description()+std::string(ADD_FILELINE)) \
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.set_num_inputs(num_parms+1) \
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.set_num_outputs(1) \
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.set_attr_parser(ParamParser<PdfParam>) \
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.set_attr<nnvm::FListInputNames>("FListInputNames", \
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[](const NodeAttrs& attrs) { \
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std::vector<std::string> v = {"sample", parm_name_1, parm_name_2}; \
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v.resize(num_parms+1); \
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return v; \
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}) \
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.set_attr<mxnet::FInferShape>("FInferShape", PdfOpShape<vectorparms>) \
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.set_attr<nnvm::FInferType>("FInferType", ElemwiseType<num_parms+1, 1>) \
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.set_attr<FCompute>("FCompute<cpu>", PdfOpForward<cpu, pdffunc, num_parms, vectorparms>) \
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.set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseInOut{"_backward_pdf_" #distr}) \
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.add_argument("sample", "NDArray-or-Symbol", "Samples from the distributions.") \
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.add_argument(parm_name_1, "NDArray-or-Symbol", parm_desc_1) \
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.add_arguments(PdfParam::__FIELDS__())
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#define MXNET_OPERATOR_REGISTER_PDF_GRAD(distr, pdffunc, num_parms, vectorparms) \
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NNVM_REGISTER_OP(_backward_pdf_##distr) \
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.set_num_inputs(num_parms+3) \
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.set_num_outputs(num_parms+1) \
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.set_attr_parser(ParamParser<PdfParam>) \
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.set_attr<nnvm::FInplaceOption>("FInplaceOption", [](const NodeAttrs& attrs) \
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{ std::vector<std::pair<int, int> > v = {{1, 0}, {2, 1}, {3, 2}}; \
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v.resize(num_parms+1); \
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return v; }) \
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.set_attr<FResourceRequest>("FResourceRequest", [](const NodeAttrs& attrs) \
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{ return std::vector<ResourceRequest>{ResourceRequest::kTempSpace}; }) \
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.set_attr<nnvm::TIsBackward>("TIsBackward", true) \
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.set_attr<FCompute>("FCompute<cpu>", PdfOpBackward<cpu, pdffunc##_Grad, num_parms, vectorparms>);
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#define MXNET_OPERATOR_REGISTER_PDF1(distr, pdffunc, parm_name, parm_desc, \
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description, vectorparms) \
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MXNET_OPERATOR_REGISTER_PDF(distr, pdffunc, 1, parm_name, parm_name, \
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parm_desc, parm_desc, description, vectorparms); \
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MXNET_OPERATOR_REGISTER_PDF_GRAD(distr, pdffunc, 1, vectorparms)
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#define MXNET_OPERATOR_REGISTER_PDF2(distr, pdffunc, parm_name_1, parm_name_2, \
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parm_desc_1, parm_desc_2, description) \
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MXNET_OPERATOR_REGISTER_PDF(distr, pdffunc, 2, parm_name_1, parm_name_2, \
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parm_desc_1, parm_desc_2, description, false) \
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.add_argument(parm_name_2, "NDArray-or-Symbol", parm_desc_2); \
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MXNET_OPERATOR_REGISTER_PDF_GRAD(distr, pdffunc, 2, false)
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inline std::string uniform_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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uniform distributions on the intervals given by *[low,high)*.
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*low* and *high* must have the same shape, which must match the leftmost subshape
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of *sample*. That is, *sample* can have the same shape as *low* and *high*, in which
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case the output contains one density per distribution, or *sample* can be a tensor
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of tensors with that shape, in which case the output is a tensor of densities such that
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the densities at index *i* in the output are given by the samples at index *i* in *sample*
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parameterized by the values of *low* and *high* at index *i*.
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Examples::
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random_pdf_uniform(sample=[[1,2,3,4]], low=[0], high=[10]) = [0.1, 0.1, 0.1, 0.1]
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sample = [[[1, 2, 3],
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[1, 2, 3]],
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[[1, 2, 3],
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[1, 2, 3]]]
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low = [[0, 0],
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[0, 0]]
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high = [[ 5, 10],
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[15, 20]]
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random_pdf_uniform(sample=sample, low=low, high=high) =
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[[[0.2, 0.2, 0.2 ],
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[0.1, 0.1, 0.1 ]],
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[[0.06667, 0.06667, 0.06667],
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[0.05, 0.05, 0.05 ]]]
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)code");
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}
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inline std::string normal_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
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*mu* and *sigma* must have the same shape, which must match the leftmost subshape
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of *sample*. That is, *sample* can have the same shape as *mu* and *sigma*, in which
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case the output contains one density per distribution, or *sample* can be a tensor
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of tensors with that shape, in which case the output is a tensor of densities such that
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the densities at index *i* in the output are given by the samples at index *i* in *sample*
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parameterized by the values of *mu* and *sigma* at index *i*.
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Examples::
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sample = [[-2, -1, 0, 1, 2]]
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random_pdf_normal(sample=sample, mu=[0], sigma=[1]) =
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[[0.05399097, 0.24197073, 0.3989423, 0.24197073, 0.05399097]]
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random_pdf_normal(sample=sample*2, mu=[0,0], sigma=[1,2]) =
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[[0.05399097, 0.24197073, 0.3989423, 0.24197073, 0.05399097],
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[0.12098537, 0.17603266, 0.19947115, 0.17603266, 0.12098537]]
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)code");
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}
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inline std::string gamma_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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gamma distributions with parameters *alpha* (shape) and *beta* (rate).
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*alpha* and *beta* must have the same shape, which must match the leftmost subshape
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of *sample*. That is, *sample* can have the same shape as *alpha* and *beta*, in which
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case the output contains one density per distribution, or *sample* can be a tensor
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of tensors with that shape, in which case the output is a tensor of densities such that
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the densities at index *i* in the output are given by the samples at index *i* in *sample*
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parameterized by the values of *alpha* and *beta* at index *i*.
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Examples::
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random_pdf_gamma(sample=[[1,2,3,4,5]], alpha=[5], beta=[1]) =
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[[0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739]]
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sample = [[1, 2, 3, 4, 5],
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[2, 3, 4, 5, 6],
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[3, 4, 5, 6, 7]]
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random_pdf_gamma(sample=sample, alpha=[5,6,7], beta=[1,1,1]) =
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[[0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739],
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[0.03608941, 0.10081882, 0.15629345, 0.17546739, 0.16062315],
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[0.05040941, 0.10419563, 0.14622283, 0.16062315, 0.14900276]]
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)code");
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}
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inline std::string exponential_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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exponential distributions with parameters *lam* (rate).
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The shape of *lam* must match the leftmost subshape of *sample*. That is, *sample*
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can have the same shape as *lam*, in which case the output contains one density per
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distribution, or *sample* can be a tensor of tensors with that shape, in which case
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the output is a tensor of densities such that the densities at index *i* in the output
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are given by the samples at index *i* in *sample* parameterized by the value of *lam*
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at index *i*.
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Examples::
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random_pdf_exponential(sample=[[1, 2, 3]], lam=[1]) =
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[[0.36787945, 0.13533528, 0.04978707]]
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sample = [[1,2,3],
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[1,2,3],
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[1,2,3]]
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random_pdf_exponential(sample=sample, lam=[1,0.5,0.25]) =
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[[0.36787945, 0.13533528, 0.04978707],
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[0.30326533, 0.18393973, 0.11156508],
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[0.1947002, 0.15163267, 0.11809164]]
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)code");
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}
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inline std::string poisson_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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Poisson distributions with parameters *lam* (rate).
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The shape of *lam* must match the leftmost subshape of *sample*. That is, *sample*
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can have the same shape as *lam*, in which case the output contains one density per
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distribution, or *sample* can be a tensor of tensors with that shape, in which case
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the output is a tensor of densities such that the densities at index *i* in the output
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are given by the samples at index *i* in *sample* parameterized by the value of *lam*
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at index *i*.
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Examples::
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random_pdf_poisson(sample=[[0,1,2,3]], lam=[1]) =
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[[0.36787945, 0.36787945, 0.18393973, 0.06131324]]
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sample = [[0,1,2,3],
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[0,1,2,3],
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[0,1,2,3]]
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random_pdf_poisson(sample=sample, lam=[1,2,3]) =
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[[0.36787945, 0.36787945, 0.18393973, 0.06131324],
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[0.13533528, 0.27067056, 0.27067056, 0.18044704],
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[0.04978707, 0.14936121, 0.22404182, 0.22404182]]
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)code");
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}
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inline std::string negative_binomial_desc() {
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return std::string(R"code(Computes the value of the PDF of samples of
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negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
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*k* and *p* must have the same shape, which must match the leftmost subshape
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of *sample*. That is, *sample* can have the same shape as *k* and *p*, in which
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case the output contains one density per distribution, or *sample* can be a tensor
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of tensors with that shape, in which case the output is a tensor of densities such that
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the densities at index *i* in the output are given by the samples at index *i* in *sample*
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parameterized by the values of *k* and *p* at index *i*.
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Examples::
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random_pdf_negative_binomial(sample=[[1,2,3,4]], k=[1], p=a[0.5]) =
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[[0.25, 0.125, 0.0625, 0.03125]]
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# Note that k may be real-valued
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sample = [[1,2,3,4],
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[1,2,3,4]]
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random_pdf_negative_binomial(sample=sample, k=[1, 1.5], p=[0.5, 0.5]) =
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[[0.25, 0.125, 0.0625, 0.03125 ],
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[0.26516506, 0.16572815, 0.09667476, 0.05437956]]
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)code");
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}
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inline std::string generalized_negative_binomial_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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generalized negative binomial distributions with parameters *mu* (mean)
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and *alpha* (dispersion). This can be understood as a reparameterization of
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the negative binomial, where *k* = *1 / alpha* and *p* = *1 / (mu \* alpha + 1)*.
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*mu* and *alpha* must have the same shape, which must match the leftmost subshape
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of *sample*. That is, *sample* can have the same shape as *mu* and *alpha*, in which
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case the output contains one density per distribution, or *sample* can be a tensor
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of tensors with that shape, in which case the output is a tensor of densities such that
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the densities at index *i* in the output are given by the samples at index *i* in *sample*
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parameterized by the values of *mu* and *alpha* at index *i*.
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Examples::
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random_pdf_generalized_negative_binomial(sample=[[1, 2, 3, 4]], alpha=[1], mu=[1]) =
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[[0.25, 0.125, 0.0625, 0.03125]]
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sample = [[1,2,3,4],
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[1,2,3,4]]
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random_pdf_generalized_negative_binomial(sample=sample, alpha=[1, 0.6666], mu=[1, 1.5]) =
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[[0.25, 0.125, 0.0625, 0.03125 ],
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[0.26517063, 0.16573331, 0.09667706, 0.05437994]]
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)code");
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}
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inline std::string dirichlet_desc() {
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return std::string(R"code(Computes the value of the PDF of *sample* of
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Dirichlet distributions with parameter *alpha*.
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The shape of *alpha* must match the leftmost subshape of *sample*. That is, *sample*
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can have the same shape as *alpha*, in which case the output contains one density per
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distribution, or *sample* can be a tensor of tensors with that shape, in which case
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the output is a tensor of densities such that the densities at index *i* in the output
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are given by the samples at index *i* in *sample* parameterized by the value of *alpha*
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at index *i*.
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Examples::
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random_pdf_dirichlet(sample=[[1,2],[2,3],[3,4]], alpha=[2.5, 2.5]) =
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[38.413498, 199.60245, 564.56085]
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sample = [[[1, 2, 3], [10, 20, 30], [100, 200, 300]],
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[[0.1, 0.2, 0.3], [0.01, 0.02, 0.03], [0.001, 0.002, 0.003]]]
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random_pdf_dirichlet(sample=sample, alpha=[0.1, 0.4, 0.9]) =
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[[2.3257459e-02, 5.8420084e-04, 1.4674458e-05],
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[9.2589635e-01, 3.6860607e+01, 1.4674468e+03]]
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)code");
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}
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MXNET_OPERATOR_REGISTER_PDF2(uniform, PDF_Uniform, "low", "high",
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"Lower bounds of the distributions.", "Upper bounds of the distributions.", uniform_desc)
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MXNET_OPERATOR_REGISTER_PDF2(normal, PDF_Normal, "mu", "sigma",
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"Means of the distributions.", "Standard deviations of the distributions.", normal_desc)
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MXNET_OPERATOR_REGISTER_PDF2(gamma, PDF_Gamma, "alpha", "beta",
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"Alpha (shape) parameters of the distributions.", "Beta (scale) parameters of the distributions.",
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gamma_desc)
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MXNET_OPERATOR_REGISTER_PDF1(exponential, PDF_Exponential, "lam",
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"Lambda (rate) parameters of the distributions.", exponential_desc, false)
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MXNET_OPERATOR_REGISTER_PDF1(poisson, PDF_Poisson, "lam",
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"Lambda (rate) parameters of the distributions.", poisson_desc, false)
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MXNET_OPERATOR_REGISTER_PDF2(negative_binomial, PDF_NegativeBinomial, "k", "p",
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"Limits of unsuccessful experiments.", "Failure probabilities in each experiment.",
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negative_binomial_desc)
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MXNET_OPERATOR_REGISTER_PDF2(generalized_negative_binomial,
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PDF_GeneralizedNegativeBinomial, "mu", "alpha",
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"Means of the distributions.", "Alpha (dispersion) parameters of the distributions.",
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generalized_negative_binomial_desc)
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MXNET_OPERATOR_REGISTER_PDF1(dirichlet, PDF_Dirichlet, "alpha",
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"Concentration parameters of the distributions.", dirichlet_desc, true)
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} // namespace op
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} // namespace mxnet

‎src/operator/random/pdf_op.cu

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/*
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* Licensed to the Apache Software Foundation (ASF) under one
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* or more contributor license agreements. See the NOTICE file
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* distributed with this work for additional information
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* regarding copyright ownership. The ASF licenses this file
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* to you under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance
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* with the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing,
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* software distributed under the License is distributed on an
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* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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* KIND, either express or implied. See the License for the
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* specific language governing permissions and limitations
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* under the License.
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*/
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/*!
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* Copyright (c) 2018 by Contributors
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* \file pdf_op.cu
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* \brief GPU-operators for computing the pdf of random distributions.
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*/
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#include "./pdf_op.h"
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namespace mxnet {
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namespace op {
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#define MXNET_OPERATOR_REGISTER_PDF(distr, pdffunc, num_parms, vector_parms) \
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NNVM_REGISTER_OP(_random_pdf_##distr) \
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.set_attr<FCompute>("FCompute<gpu>", PdfOpForward<gpu, pdffunc, num_parms, vector_parms>); \
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NNVM_REGISTER_OP(_backward_pdf_##distr) \
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.set_attr<FCompute>("FCompute<gpu>", PdfOpBackward<gpu, pdffunc##_Grad, num_parms, vector_parms>);
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MXNET_OPERATOR_REGISTER_PDF(uniform, PDF_Uniform, 2, false)
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MXNET_OPERATOR_REGISTER_PDF(normal, PDF_Normal, 2, false)
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MXNET_OPERATOR_REGISTER_PDF(gamma, PDF_Gamma, 2, false)
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MXNET_OPERATOR_REGISTER_PDF(exponential, PDF_Exponential, 1, false)
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MXNET_OPERATOR_REGISTER_PDF(poisson, PDF_Poisson, 1, false)
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MXNET_OPERATOR_REGISTER_PDF(negative_binomial, PDF_NegativeBinomial, 2, false)
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MXNET_OPERATOR_REGISTER_PDF(generalized_negative_binomial,
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PDF_GeneralizedNegativeBinomial, 2, false)
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MXNET_OPERATOR_REGISTER_PDF(dirichlet, PDF_Dirichlet, 1, true)
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} // namespace op
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} // namespace mxnet

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