A2021
Title: Robust high-dimensional multivariate regression with non-Gaussian errors via global-local shrinkage priors
Authors: Dongu Han - Meiji University (Japan) [presenting]
Jichan Park - Korea University (Korea, South)
Genya Kobayashi - School of Commerce, Meiji University (Japan)
Taeryon Choi - Korea University (Korea, South)
Abstract: High-dimensional multivariate regression models that rely on Gaussian error assumptions are often sensitive to outliers and distributional skewness, which limits their practical applicability. To address this limitation, a robust multivariate Bayesian regression framework that replaces the Gaussian error distribution with flexible alternatives, including the multivariate-t, skew-normal, and skew-t distributions is proposed. To accommodate high-dimensional settings in which the number of parameters exceeds the sample size, horseshoe+ priors are imposed on both the regression coefficients and the off-diagonal elements of the precision matrix. This specification induces joint sparsity in the regression structure and the conditional dependence graph. For posterior computation, efficient Gibbs sampling algorithms are developed that exploit scale-mixture representations of the non-Gaussian error distributions and an alternative mean-field variational Bayes approximation that substantially reduces computational cost. Posterior and variable selection consistency are established, a tighter Kullback-Leibler risk bound over the standard horseshoe prior is derived, and robustness to unbounded outliers under the multivariate-t models is demonstrated. Simulation studies, along with applications to macroeconomic and cancer genomics datasets, demonstrate that the proposed method outperforms state-of-the-art competitors in estimation accuracy and predictive performance.
