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.