B1450
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 a flexible class of probabilistic non-parametric function models. Vecchia approximations are accurate and fast for GPs to overcome computational bottlenecks for large sample sizes. The Laplace approximation is a fast method to approximate marginal likelihoods and posterior predictive distributions for latent GPs with asymptotic convergence guarantees. Unfortunately, the computational costs of combined Vecchia-Laplace approximations grow faster than linear 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 developed for Vecchia-Laplace approximations that scale linearly in time and memory cost. The novel methods are analyzed and compared in experiments with simulated and real-world data. All methods are implemented in a free C++ software library with Python and R interface packages.
