Hybrid Best Subset Selection for Bayesian Multivariate Regression

Abstract

Multivariate linear regression has been widely studied and applied across many scientific fields. The rapid growth of high-dimensional data has increased demand for fast and accurate variable selection methods in multivariate regression. This paper proposes a Bayesian best subset selection approach that efficiently searches for optimal solutions to nonconvex optimization problems arising in high-dimensional multivariate linear regression. The proposed method employs a hybrid search strategy that integrates deterministic local optimization with stochastic global exploration, with an asymptotic global-convergence guarantee for the fixed-size search as the number of stochastic iterations increases. To accelerate implementation, we develop a fast computing strategy that evaluates the marginal posterior distributions of all neighboring models within a single computation. Simulation studies and real data analyses demonstrate the effectiveness and superior performance of the proposed approach.