Mean Field Approximation in Bayesian Variable Selection

TL;DR

This paper applies mean field approximation to Bayesian variable selection in regression models, enabling efficient estimation of relevant variables with an application to Boston housing data.

Contribution

It introduces a mean field approximation method for Bayesian variable selection, providing a new approach to estimate discrete model parameters efficiently.

Findings

Effective variable selection demonstrated on Boston housing data

Mean field approximation yields accurate posterior estimates

Method improves computational efficiency in Bayesian variable selection

Abstract

Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset of the explanatory variables. Then, a mean field approximation is introduced for the calculation of the posterior averages over the discrete parameters. An application to a real world example, Boston housing data, is shown.