Sequential Bayesian kernel modelling with non-Gaussian noise

Abstract

This paper presents a sequential Bayesian approach to kernel modelling of data, which contain unusual observations and outliers. The noise is heavy tailed described as a one-dimensional mixture distribution of Gaussians. The development uses a factorised variational approximation to the posterior of all unknowns, that helps to perform tractable Bayesian inference at two levels: (1) sequential estimation of the weights distribution (including its mean vector and covariance matrix); and (2) recursive updating of the noise distribution and batch evaluation of the weights prior distribution. These steps are repeated, and the free parameters of the non-Gaussian error distribution are adapted at the end of each cycle. The reported results show that this is a robust approach that can outperform standard methods in regression and time-series forecasting.