A0427
Title: Iterative methods for Vecchia-Laplace approximations for latent Gaussian process models
Authors: Pascal Kuendig - Lucerne University of Applied Sciences and Arts (Switzerland) [presenting]
Fabio Sigrist - ETH Zurich (Switzerland)
Abstract: Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, i.e., on large data sets. Iterative methods are presented to overcome this drawback. Among other things, several preconditioners are introduced and analyzed, new convergence results are derived, and novel methods are proposed for accurately approximating predictive variances. The proposed methods are analyzed theoretically and in experiments with simulated and real-world data. In particular, a speed-up of an order of magnitude compared to Cholesky-based calculations and a threefold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite data set are obtained.
