Gaussian Process

Novi Quadrianto, Kristian Kersting, Zhao Xu

Abstract:

Expectation propagation; Kernels; Laplace estimate; Nonparametric Bayesian
Gaussian processes generalize multivariate Gaussian distributions over finite-dimensional vectors to infinite dimensionality. Specifically, a Gaussian process is a stochastic process that has Gaussian-distributed finite-dimensional marginal distributions, hence the name. In doing so, it defines a distribution over functions, i.e., each draw from a Gaussian process is a function. Gaussian processes provide a principled, practical, and probabilistic approach to inference and learning in kernel machines.
Bayesian probabilistic approaches have many virtues, including their ability to incorporate prior knowledge and their ability to link related sources of information. Typically, we are given a set of data points sampled from an underlying but unknown distribution, each of which includes input x and output y, such as the ones shown in Fig. 1a. The task is to learn a...