63: Weighted Bayesian Bootstrap for Reduced Rank Regression with Singular Value Decomposition

Music City Center 

Bayesian Reduced Rank Regression (RRR) has attracted increasing attention as a means to quantify the uncertainty of both the coefficient matrix and its rank in a multivariate linear regression framework. However, the existing Bayesian RRR approach relies on the strong assumption that the positions of independent coefficient vectors are known when the rank of the coefficient matrix is given. In contrast, the conventional RRR approach is free from this assumption since it permits the singular value decomposition (SVD) of the coefficient matrix. In this paper, we propose a Weighted Bayesian Bootstrap (WBB) approach to incorporate the SVD into the Bayesian RRR framework. The proposed Bayesian method offers an innovative way of sampling from the posterior distribution of the low-rank coefficient matrix. In addition, our WBB approach allows simultaneous posterior sampling for all ranks, which greatly improves computational efficiency. To quantify the rank uncertainty, we develop a posterior sample-based Monte Carlo method for marginal likelihood calculation. We demonstrate the superiority and applicability of the proposed method by conducting simulation studies and real data analysis.

Bayesian Reudced Rank Regression

Singular Value Decomposition

Weighted Bayesian Bootstrap

Bayes factors 

Korean International Statistical Society