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

TL;DR

This paper introduces a message passing framework for fast, scalable approximate inference in large Bayesian semiparametric regression models, leveraging factor graph representations for efficient computation.

Contribution

It develops a general message passing approach based on mean field variational Bayes and factor graphs, enabling scalable inference in large semiparametric models.

Findings

Algorithms have closed-form expressions for implementation.

Approach handles arbitrarily large models efficiently.

Framework applicable to general Bayesian hierarchical models.

Abstract

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.