Sparse Multivariate Factor Regression Models and Its Application to High-Throughput Array Data Analysis

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yan Zhou*+ and Peter X.K. Song and Ji Zhu
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Association analysis ; High dimensional data ; Latent factors ; EM-groupwise coordinate descent ; Regularization

Abstract

The sparse multivariate regression model is a useful tool to explore complex associations between multiple response variables and multiple predictors. When those multiple responses are strongly correlated, ignoring such dependency will impair statistical power and accuracy in the association analysis. Motivated primarily with the objective regarding evaluation of genetic association, we propose a new methodology--sparse multivariate factor regression model, in which correlations of the response variables are specified by a factor model with latent factors. This proposed method not only allows us to address the challenge that the number of regression parameters is much larger than the sample size, but also to adjust for unobserved genetic or non-genetic factors that potentially obscure real response-predictor associations. The proposed sMFRM is implemented efficiently by utilizing strength of the EM algorithm and the group-wise coordinate descend algorithm. The efficacy of the proposed methodology in unveiling the underlying response-predictor associations is evaluated through extensive simulation studies and the real breast cancer data analysis.