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

Aki Vehtari, Tommi Mononen, Ville Tolvanen, Tuomas Sivula, Ole Winther

Research output: Contribution to journalArticleScientificpeer-review

36 Citations (Scopus)
48 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1-38
Number of pages38
JournalJournal of Machine Learning Research
Publication statusPublished - 1 Jun 2016
MoE publication typeA1 Journal article-refereed


  • Expectation propagation
  • Gaussian latent variable model
  • Laplace approximation
  • Leave-one-out cross-validation
  • Predictive performance


Dive into the research topics of 'Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models'. Together they form a unique fingerprint.

Cite this