[Docs] Multi-task (multi-classification + regression)

[ChihYuLee]

Hi I am wondering if there's an example of combining multi-classification and regression problem into linear coregionalization model? My input features are 2 dimensional output is 1D regression + 1D 3-classes categories.
My problem is defined as:

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I am wondering if there is a way we can combine multi-class classification with regression. I probably need to write a CategoricalLikelihood().
My input features are 2 dimensional output is 1D regression + 1D 3-classes categories.
My current code is:

np.random.seed(42)
n_samples = 100
X1 = np.random.rand(n_samples) * 10
X2 = np.random.rand(n_samples) * 10

y_regression = 3 * X1 + 2 * X2 + np.random.randn(n_samples) * 2
y_classification = np.digitize(y_regression, bins=[-np.inf, 10, 25, np.inf]) - 1
y_classification = y_classification.astype(int)
y_regression = np.array([2.5 if label == 0 else 0.5 if label == 1 else 1.5 for label in y_classification])+np.random.randn(n_samples) * 2 *0.1

plt.figure(figsize=(4, 3))
plt.scatter(X1,X2, c=y_regression)
plt.title('Regression')
plt.colorbar()

plt.figure(figsize=(4, 3))
plt.scatter(X1,X2, c=y_classification)
plt.title('Classification')

X = np.hstack([X1[:,None], X2[:,None]])
y = np.hstack([y_regression[:,None], y_classification[:,None]])
X_train = torch.from_numpy(X).float()
y_train=torch.tensor(y)

num_latents = X_train.shape[1]
num_tasks = y_train.shape[1]
num_classes= 3

I have referred to some discussion and examples, still quite not sure where I should start.
#1396
https://github.com/cornellius-gp/gpytorch/blob/main/examples/03_Multitask_Exact_GPs/Hadamard_Multitask_GP_Regression.ipynb
https://docs.gpytorch.ai/en/stable/examples/04_Variational_and_Approximate_GPs/SVGP_Multitask_GP_Regression.html
I would appreciate any hints.