Stochastic Expectation Propagation

This is the final version of the article. It first appeared from Neural Information Processing Systems Foundation via http://papers.nips.cc/paper/5760-stochastic-expectation-propagationExpectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference (VI), and is the method of choice for a number of models. The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale dataset settings. However, EP has a crucial limitation in this context: the number of approximating factors needs to increase with the number of datapoints, N, which often entails a prohibitively large memory overhead. This paper presents an extension to EP, called stochastic expectation propagation (SEP), that maintains a global posterior approximation (like VI) but updates it in a local way (like EP). Experiments on a number of canonical learning problems using synthetic and real-world datasets indicate that SEP performs almost as well as full EP, but reduces the memory consumption by a factor of N. SEP is therefore ideally suited to performing approximate Bayesian learning in the large model, large dataset setting.We thank the reviewers for valuable comments. YL thanks the Schlumberger Foundation Faculty for the Future fellowship on supporting her PhD study. JMHL acknowledges support from the Rafael del Pino Foundation. RET thanks EPSRC grant # EP/G050821/1 and EP/L000776/1