Approximate Inference for Nonstationary Heteroscedastic Gaussian process Regression

TL;DR

This paper introduces an efficient EP-based method for approximate inference in nonstationary heteroscedastic Gaussian process regression, effectively handling input-dependent noise and signal variances with comparable accuracy to MCMC but at lower computational cost.

Contribution

It proposes a novel, straightforward EP-based approach for integrating over noise and signal variances in nonstationary heteroscedastic GP regression, improving efficiency.

Findings

EP achieves results comparable to MCMC

Method reduces computational burden

Effective in simulated and empirical data

Abstract

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal variance (nonstationarity) by setting independent GP priors for the noise and signal variances. We use expectation propagation (EP) for inference and compare results to Markov chain Monte Carlo in two simulated data sets and three empirical examples. The results show that EP produces comparable results with less computational burden.