In this work, we concentrate on the Bayesian structure selection problems for the categorical response. We focus on solving the selection problem for multiple binary responses and use the probit model for each response. Here, we consider the group structure with sparsity property on the rows of coefficient matrix where each row corresponds to one variable. Then we identify the relevant variables for the responses and the selection problems can be treated as the multi-task learning problem. The effectiveness of our proposed method will be demonstrated through simulation studies.

Keyword: Multi-task learning, component-wise algorithm, group structure, Markov chain Monte Carlo