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We show how the notion of message passing can be used to streamline thealgebra and computer coding for fast approximate inference in large Bayesiansemiparametric regression models. In particular, this approach is amenable tohandling arbitrarily large models of particular types once a set of primitiveoperations is established. The approach is founded upon a message passingformulation of mean field variational Bayes that utilizes factor graphrepresentations of statistical models. The underlying principles apply togeneral Bayesian hierarchical models although we focus on semiparametricregression. The notion of factor graph fragments is introduced and is shown tofacilitate compartmentalization of the required algebra and coding. Theresultant algorithms have ready-to-implement closed form expressions and allowa broad class of arbitrarily large semiparametric regression models to behandled. Ongoing software projects such as Infer.NET and Stan supportvariational-type inference for particular model classes. This article is notconcerned with software packages per se and focuses on the underlying tenets ofscalable variational inference algorithms.

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