Quantile Propagation for Wasserstein-Approximate Gaussian Processes

Abstract

We develop a new approximate Bayesian inference method for Gaussian process models with factorized non-Gaussian likelihoods. Our method---dubbed Quantile Propagation (QP)---is similar to expectation propagation (EP) but minimizes the L_2 Wasserstein distance rather than the Kullback-Leibler (KL) divergence. We consider the case where likelihood factors are approximated by a Gaussian form. We show that QP matches quantile functions rather than moments as in EP and has the same mean update but a smaller variance update than EP, thereby alleviating the over-estimation of the posterior variance exhibited by EP. Crucially, QP has the same favorable locality property as EP, and thereby admits an efficient algorithm. Experiments on classification and Poisson regression tasks demonstrate that QP outperforms both EP and variational Bayes