How come the StudentTLikelihood is 10 dimensional?

[SebastianCallh]

I would expect it to be 1-dimensional for 1-dimensional observations but I'm guessing there is a good reason for the (to me) surprising behaviour. Can anyone please explain this to me? Thanks! See the snippet below for an example.

import gpytorch
import torch

class GPModel(gpytorch.models.ApproximateGP):
    def __init__(self, inducing_points):
        variational_distribution = gpytorch.variational.NaturalVariationalDistribution(inducing_points.size(0))
        variational_strategy = gpytorch.variational.VariationalStrategy(
            self, inducing_points, variational_distribution, learn_inducing_locations=True
        )
        super(GPModel, self).__init__(variational_strategy)
        self.mean_module = gpytorch.means.ConstantMean()
        self.covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())

    def forward(self, x):
        mean_x = self.mean_module(x)
        covar_x = self.covar_module(x)
        return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)


x = torch.linspace(0, 10, 100)
model = GPModel(inducing_points=x)
likelihood = gpytorch.likelihoods.StudentTLikelihood()

model(x).mean.shape # torch.Size([100]), nothing out of the ordinary here
likelihood(model(x)).mean.shape # torch.Size([10, 100]), surprising!

[gpleiss]

See the documentation (currently available only under "latest", will be under "stable" upon next release): https://docs.gpytorch.ai/en/latest/likelihoods.html#gpytorch.likelihoods.Likelihood.__call__

Also see #1955 for a discussion on this topic.

[SebastianCallh]

Thank you! I didn't realise the likelihood Monte Carlo sampled automatically 👍