Reduced-Rank Stochastic Regression with a Sparse Singular-Value-Decomposition: Modeling Larval Drift Effects on Cod Population Dynamics as a Case Study

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Kun Chen*+ and Kung-Sik Chan and Nils Christian Stenseth
• Companies: The University of Iowa and The University of Iowa and Centre for Ecological and Evolutionary Synthesis
• Keywords: Reduced-rank ; Multivariate ; Stochastic Regression ; L1 Regularization ; Bilinear

Abstract

For a reduced-rank multivariate stochastic regression model of, say, rank r, the regression coefficient matrix can be expressed as a sum of r unit-rank matrices each of which is proportional to the outer-product of the left and right singular vectors. For facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose an L1-regularized bilinear regression approach for solving the afore-mentioned problem. Computation algorithm and tuning parameter selection methods are developed, and the properties of the new method are explored both theoretically and by simulation. We apply the proposed approach to analyzing the Norwegian Skagerrak coastal cod abundance data for simultaneously capturing the important spawning window and identifying significant North Sea larval drift effects among coastal fjords.