Robust weighted Gaussian processes

Abstract

This paper presents robust weighted variants of batch and online standard Gaussian processes (GPs) to effectively reduce the negative impact of outliers in the corresponding GP models. This is done by introducing robust data weighers that rely on robust and quasi-robust weight functions that come from robust M-estimators. Our robust GPs are compared to various GP models on four datasets. It is shown that our batch and online robust weighted GPs are indeed robust to outliers, significantly outperforming the corresponding standard GPs and the recently proposed heteroscedastic GP method GPz. Our experiments also show that our methods are comparable to and sometimes better than a state-of-the-art robust GP that uses a Student-t likelihood.