An Approximated Collapsed Variational Bayes Approach to Variable Selection in Linear Regression

Chong You, John T. Ormerod, Xiangyang Li, Cheng Heng Pang & Xiao-Hua Zhou
In this work, we propose a novel approximated collapsed variational Bayes approach to model selection in linear regression. The approximated collapsed variational Bayes algorithm offers improvements over mean field variational Bayes by marginalizing over a subset of parameters and using mean field variational Bayes over the remaining parameters in an analogous fashion to collapsed Gibbs sampling. We have shown that the proposed algorithm, under typical regularity assumptions, (a) includes variables in the true underlying model...
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