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

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we describe the properties of several Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models where the integration over the latent values is made using the Laplace method or expectation propagation. These leave-one-out cross-validation approximations can be computed with a small additional cost after forming the posterior approximation given the whole data. We show that that model specific approximations provide accurate and more reliable results than generic approaches.