Open Access
June 2019 Variational Message Passing for Elaborate Response Regression Models
M. W. McLean, M. P. Wand
Bayesian Anal. 14(2): 371-398 (June 2019). DOI: 10.1214/18-BA1098


We build on recent work concerning message passing approaches to approximate fitting and inference for arbitrarily large regression models. The focus is on regression models where the response variable is modeled to have an elaborate distribution, which is loosely defined to mean a distribution that is more complicated than common distributions such as those in the Bernoulli, Poisson and Normal families. Examples of elaborate response families considered here are the Negative Binomial and t families. Variational message passing is more challenging due to some of the conjugate exponential families being non-standard and numerical integration being needed. Nevertheless, a factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family. Computer code can be compartmentalized, including that involving numerical integration. A major finding of this work is that the modularity of variational message passing extends to elaborate response regression models.


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M. W. McLean. M. P. Wand. "Variational Message Passing for Elaborate Response Regression Models." Bayesian Anal. 14 (2) 371 - 398, June 2019.


Published: June 2019
First available in Project Euclid: 25 May 2018

zbMATH: 07045435
MathSciNet: MR3934090
Digital Object Identifier: 10.1214/18-BA1098

Primary: 62F15 , 62J05
Secondary: 62G08

Keywords: Bayesian computing , factor graph , generalized additive models , generalized linear mixed models , Mean field variational Bayes , support vector machine classification

Vol.14 • No. 2 • June 2019
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