Tilted variational Bayes

We present a novel method for approximate inference. Using some of the constructs from expectation propagation (EP), we derive a lower bound of the marginal likelihood in a similar fashion to variational Bayes (VB). The method combines some of the benefits of VB and EP: it can be used with light-tailed likelihoods (where traditional VB fails), and it provides a lower bound on the marginal likelihood. We apply the method to Gaus-sian process classification, a situation where the Kullback-Leibler divergence minimized in traditional VB can be infinite, and to robust Gaussian process regression, where the in-ference process is dramatically simplified in comparison to EP. Code to reproduce all the experiments can be found at github.com/SheffieldML/TVB.