Sparse Point Estimation for Bayesian Regression via Simulated Annealing

Abstract

In the context of variable selection in a regression model, the classical Lasso based optimization approach provides a sparse estimate with respect to regression coefficients but is unable to provide more information regarding the distribution of regression coefficients. Alternatively, using a Bayesian approach is more advantageous since it gives direct access to the distribution which is usually summarized by estimating the expectation (not sparse) and variance. Additionally, to support frequent application requirements, heuristics like thresholding are generally used to produce sparse estimates for variable selection purposes. In this paper, we provide a more principled approach for generating a sparse point estimate in a Bayesian framework. We extend an existing Bayesian framework for sparse regression to generate a MAP estimate by using simulated annealing. We then justify this extension by showing that this MAP estimate is also sparse in the regression coefficients. Experiments on real world applications like the splice site detection and diabetes progression demonstrate the usefulness of the extension.