Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 112, Issue 517, Pages 137-156Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2016.1197833
Keywords
Factor graphs; Generalized additive models; Generalized linear mixed models; Low-rank smoothing splines; Mean field variational Bayes; Scalable statistical methodology; Variational message passing
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Funding
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers
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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.
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