marginal_log_likelihoods.rst

gpytorch.mlls

These are modules to compute (or approximate/bound) the marginal log likelihood (MLL) of the GP model when applied to data. I.e., given a GP f ∼ 𝒢𝒫(μ, K), and data X, y, these modules compute/approximate

ℒ = p_f(y​∣​X) = ∫p(y​∣​f(X)) p(f(X)​∣​X) df

This is computed exactly when the GP inference is computed exactly (e.g. regression w/ a Gaussian likelihood). It is approximated/bounded for GP models that use approximate inference.

These models are typically used as the "loss" functions for GP models (though note that the output of these functions must be negated for optimization).

gpytorch.mlls

gpytorch.mlls

Exact GP Inference

These are MLLs for use with ~gpytorch.models.ExactGP modules. They compute the MLL exactly.

ExactMarginalLogLikelihood

ExactMarginalLogLikelihood

LeaveOneOutPseudoLikelihood

LeaveOneOutPseudoLikelihood

Approximate GP Inference

These are MLLs for use with ~gpytorch.models.ApproximateGP modules. They are designed for when exact inference is intractable (either when the likelihood is non-Gaussian likelihood, or when there is too much data for an ExactGP model).

VariationalELBO

VariationalELBO

PredictiveLogLikelihood

PredictiveLogLikelihood

GammaRobustVariationalELBO

GammaRobustVariationalELBO

DeepApproximateMLL

DeepApproximateMLL

Modifications to Objective Functions

AddedLossTerm

InducingPointKernelAddedLossTerm

InducingPointKernelAddedLossTerm

KLGaussianAddedLossTerm

KLGaussianAddedLossTerm