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Weighted Bayesian Bootstrap for Reduced Rank Regression with Singular Value Decomposition

Abstract Number:

1141 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Poster 

Participants:

Wonbin Jung (1), Hyeonji Shin (1), Hyewon Oh (1), Yeonsu Lee (1), Minseok Kim (1), Seongyun Kim (1), Gyuhyeong Goh (2)

Institutions:

(1) Kyungpook National University, N/A, (2) Department of Statistics, Kyungpook National University, N/A

Co-Author(s):

Hyeonji Shin  
Kyungpook National University
Hyewon Oh  
Kyungpook National University
Yeonsu Lee  
Kyungpook National University
Minseok Kim  
Kyungpook National University
Seongyun Kim  
Kyungpook National University
Gyuhyeong Goh  
Department of Statistics, Kyungpook National University

First Author:

Wonbin Jung  
Kyungpook National University

Presenting Author:

Wonbin Jung  
Kyungpook National University

Abstract Text:

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.

Keywords:

Bayesian Reudced Rank Regression|Singular Value Decomposition|Weighted Bayesian Bootstrap|Bayes factors| |

Sponsors:

Korean International Statistical Society

Tracks:

Miscellaneous

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