CS535D Project: Bayesian Logistic Regression through Auxiliary Variables

This project deals with the estimation of Logistic Regression parameters. We first review the binary logistic regression model and the multinomial extension, including standard MAP parameter estimation with a Gaussian prior. We then turn to the case of Bayesian Logistic Regression under this same prior. We review the cannonical approach of performing Bayesian Probit Regression through auxiliary variables, and extensions of this technique to Bayesian Logistic Regression and Bayesian Multinomial Regression. We then turn to the task of feature selection, outlining a trans-dimensional MCMC approach to variable selection in Bayesian Logistic Regression. Finally, we turn to the case of estimating MAP parameters and performing Bayesian Logistic Regression under L1 penalties and other sparsity promoting priors.