Nonstationary Gaussian process regression using point estimates of local smoothness

Abstract

Gaussian processes using nonstationary covariance functions are a powerful tool for Bayesian regression with input-dependent smoothness. A common approach is to model the local smoothness by a latent process that is integrated over using Markov chain Monte Carlo approaches. In this paper, we demonstrate that an approximation that uses the estimated mean of the local smoothness yields good results and allows one to employ efficient gradient-based optimization techniques for jointly learning the parameters of the latent and the observed processes. Extensive experiments on both synthetic and real-world data, including challenging problems in robotics, show the relevance and feasibility of our approach. © 2008 Springer-Verlag Berlin Heidelberg.