Abstract

In this talk I will cover two topics on Gaussian process learning. First, I will describe tensor-variate latent nonparametric Bayesian models, coupled with efficient inference methods, for multiway data analysis. Unlike classical tensor decomposition models, our new approaches model nonlinear interactions and handle both continuous and binary data. To efficiently learn the InfTucker from data, we develop a variational inference technique on tensors. Compared with classical implementation, the new technique reduces both time and space complexities by several orders of magnitude. Our experimental results on chemometrics and social network datasets demonstrate that our new models can achieve significantly higher prediction accuracy than state-of-art tensor decomposition approaches. Furthermore, for two dimensional problems, our tensor model reduces to nonlinear stochastic blockmodels for network modeling, which I will briefly discuss in the talk as well. Second, I will describe a new sparse Gaussian process model, EigenGP, based on Karhunen-Loeve (KL) expansions of a GP prior. We can view this new approach as sparse PCA in a functional space, which not only reduces the computational cost of GP inference but also has the potential of further improving the predictive performance of a full GP. By selecting eigenfunctions of Gaussian kernels that are associated with data clusters, EigenGP is also suitable for semi-supervised learning. Our experimental results demonstrate improved predictive performance of EigenGP over several state-of-the- art sparse GP and semisupervised learning methods for regression, classification, and semisupervised classification.