Uncertainty Bounds for Kernel-based Regression: a Bayesian SPS Approach

Algo Carè, Gianluigi Pillonetto, Marco C. Campi

Abstract: This paper shows that kernel-based estimates of unknown input-output maps can be complemented with uncertainty bounds more robust than those commonly derived in the Gaussian regression framework. This is obtained by using the kernel not to define Gaussian priors but a much vaster class of symmetric distributions. Such class is then handled by extending to the Bayesian setting the recently developed sign-perturbed sums (SPS) framework.