Expectation propagation in the large data limit

• 成果类型: Article
• 署名作者: Dehaene, Guillaume; Barthelme, Simon
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Geneva
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12241
• 发表日期: 2018
• 页码: 199-217
• 关键词: approximate inference; INEQUALITY

摘要

Expectation propagation (EP) is a widely successful algorithm for variational inference. EP is an iterative algorithm used to approximate complicated distributions, typically to find a Gaussian approximation of posterior distributions. In many applications of this type, EP performs extremely well. Surprisingly, despite its widespread use, there are very few theoretical guarantees on Gaussian EP, and it is quite poorly understood. To analyse EP, we first introduce a variant of EP: averaged EP, which operates on a smaller parameter space. We then consider averaged EP and EP in the limit of infinite data, where the overall contribution of each likelihood term is small and where posteriors are almost Gaussian. In this limit, we prove that the iterations of both averaged EP and EP are simple: they behave like iterations of Newton's algorithm for finding the mode of a function. We use this limit behaviour to prove that EP is asymptotically exact, and to obtain other insights into the dynamic behaviour of EP, e.g. that it may diverge under poor initialization exactly like Newton's method. EP is a simple algorithm to state, but a difficult one to study. Our results should facilitate further research into the theoretical properties of this important method.