Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models

TL;DR

This paper evaluates the accuracy of Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models, comparing methods like Laplace and expectation propagation against exact computations and MCMC ground truth.

Contribution

It provides a comprehensive assessment of LOO approximation methods for Gaussian latent variable models, highlighting the most accurate approach among fast alternatives.

Findings

Gaussian approximation to the LOO marginal distribution is most accurate

Fast LOO methods closely match exact computations in most cases

Laplace and EP approximations are validated against MCMC ground truth

Abstract

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several Bayesian leave-one-out (LOO) cross-validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data. Our main objective is to assess the accuracy of the approximative LOO cross-validation estimators. That is, for each method (Laplace and EP) we compare the approximate fast computation with the exact brute force LOO computation. Secondarily, we evaluate the accuracy of the Laplace and EP approximations themselves against a ground truth established through extensive Markov chain Monte Carlo simulation. Our empirical results show that the approach based upon a Gaussian approximation to the LOO marginal distribution (the so-called cavity distribution) gives the most accurate and reliable results among the fast methods.