Kun Chen ColloquiumThursday, March 31, 2016 - 2:45pm
Statistics Department Colloquium
Where: LeConte College, Room 210
Speaker: Kun Chen
Affiliation: University of Connecticut, Department of Statistics
Title: Sequential Estimation in Sparse Factor Regression
Abstract: Multivariate regression models of large scales are increasingly required and formulated in various fields. A sparse singular value decomposition of the regression component matrix is appealing for achieving dimension reduction and facilitating model interpretation. However, how to recover such a composition of sparse and low-rank structures remains a challenging problem. By exploring the connections between factor analysis and reduced-rank regression, we formulate the problem as a sparse factor regression and develop an efficient sequential estimation procedure. At each sequential step, a latent factor is constructed as a sparse linear combination of the observed predictors, for predicting the responses after adjusting for the effects of the previously found latent factors. Each sequential step reduces to a regularized unit-rank regression; when exact orthogonality among the sparse factors is desirable, it can be conveniently achieved through linear constrained optimization. The ideas of coordinate descent and Bregman iterative methods are utilized to ensure fast computation and algorithmic convergence even in the presence of missing data. Theoretically, we show that the sequential estimators enjoy the oracle properties for recovering the underlying sparse factor structure. The efficacy of the proposed approach is demonstrated by simulation studies and two real applications in genetics.