Bayesian Leave-One-Out Cross-Validation Approximations for Gaussian Latent Variable Models

Aki Vehtari, Tommi Jouni Mikael Mononen, Ville Tolvanen, Tuomas Antti Pietari Sivula, Ole Winther

Tutkimustuotos: ArtikkelijulkaisuArtikkeliTieteellinenvertaisarvioitu

Abstrakti

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.
Alkuperäiskielienglanti
LehtiJournal of Machine Learning Research
Vuosikerta17
Numero103
Sivut1-38
Sivumäärä38
ISSN1532-4435
TilaJulkaistu - 2016
Julkaistu ulkoisestiKyllä
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä, vertaisarvioitu

Tieteenalat

  • 213 Sähkö-, automaatio- ja tietoliikennetekniikka, elektroniikka

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