  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.
