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The Information Systems and Statistics Research Seminar Series
Presented by the Paul H. Chook Department of Information Systems and Statistics
“Stagewise Co-Sparse and Low-Rank Matrix Factorization”
Kun Chen, Assistant Professor, University of Connecticut
Thursday, May 3, 2018 @ 12:30pm-1:45pm
NVC 11-217, ISS Conference Room
From: Prof. Rongning Wu, Paul H. Chook Department of Information Systems and Statistics
We consider the problem of obtaining a sparse singular value decomposition (SSVD) of a matrix. This SSVD structure is very appealing, particularly in high-dimensional multivariate regression and factor analysis, as it implies that the outcomes are related to the features through a few distinct pathways, each of which may only involve a subset of the outcomes and the features. However, many existing computational methods involve repeated SVD operations and/or orthogonality constraints, rendering them unsuitable for large-scale problems. We take a divide-and-conquer strategy to tackle the problem. By delving into the statistical data generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, which enables us to simplify the task into a set of co-sparse unit-rank regression problems. We show that the resulting estimators are consistent and enjoy the oracle properties asymptotically. To make the computation scalable, for the co-sparse unit-rank regression, we innovate a stagewise estimation procedure to efficiently trace out its entire solution path. We show that as the step size goes to zero, the stagewise solution paths converge exactly to those of the corresponding penalized regression. Extension to tensor decomposition and generalized eigenvalue problems will be discussed.
Paul H. Chook Department of Information Systems and Statistics