Fast Approximate Inference for Arbitrarily Large Semiparametric Regression Models via Message Passing

• Published in: Journal of the American Statistical Association Vol. 112; no. 517; pp. 137 - 168
• Main Author: Wand, M. P.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.01.2017; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Algebra; Algorithms; Bayesian analysis; Coding; computer software; computers; equations; Factor graphs; Fragments; Generalized additive models; Generalized linear mixed models; Graph representations; Graphical representations; Inference; Low-rank smoothing splines; Mathematical analysis; Mean field variational Bayes; Message passing; Regression analysis; Regression models; Scalable statistical methodology; Software packages; Statistical analysis; Statistical methods; Statistical models; Statistics; Theory and Methods; Variational message passing
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2016.1197833

We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling arbitrarily large models of particular types once a set of primitive operations is established. The approach is founded upon a message passing formulation of mean field variational Bayes that utilizes factor graph representations of statistical models. The underlying principles apply to general Bayesian hierarchical models although we focus on semiparametric regression. The notion of factor graph fragments is introduced and is shown to facilitate compartmentalization of the required algebra and coding. The resultant algorithms have ready-to-implement closed form expressions and allow a broad class of arbitrarily large semiparametric regression models to be handled. Ongoing software projects such as Infer.NET and Stan support variational-type inference for particular model classes. This article is not concerned with software packages per se and focuses on the underlying tenets of scalable variational inference algorithms. Supplementary materials for this article are available online.