Bayesian Fused Lasso Modeling for Binary Data

Abstract: L1-norm regularized logistic regression models are widely used for analyzing data with binary response. In those analyses, fusing regression coefficients is useful for detecting groups of variables. This paper proposes a binomial logistic regression model with Bayesian fused lasso. Assuming a Laplace prior on regression coefficients and differences between adjacent regression coefficients enables us to perform variable selection and variable fusion simultaneously in the Bayesian framework. We also propose assuming a horseshoe prior on the differences to improve the flexibility of variable fusion. The Gibbs sampler is derived to estimate the parameters by a hierarchical expression of priors and a data-augmentation method. Using simulation studies and real data analysis, we compare the proposed methods with the existing method.