VARIATIONAL BAYES METHODS IN GAUSSIAN PROCESS REGRESSION

Abstract

The increasing availability of large datasets in many scientific applications has resulted in a great deal of interest recently in fast approximate inference methods that facilitate the fitting of flexible models to these data. This thesis addresses these interests by considering fast scalable variational Bayes methods for fitting several hierarchical Gaussian process regression models. Models considered comprise unconstrained Gaussian process regression models, monotone shape restricted Gaussian process regression models, monotone concave or convex shape restricted Gaussian process regression models, functional models for longitudinal data with covariate dependent smoothness, and Gaussian process mixtures. Spectral approximations are considered for the Gaussian process terms to facilitate the development of the fitting algorithms. The utility of variational Bayes methods in comparison with appropriate MCMC methods is illustrated in model fitting, model selection and computational savings in terms of computation time.