Regularization, Sparsity, and Rank Restrictions in High-Dimensional Regression

• Activity Number: 589
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Alan Julian Izenman*+
• Companies: Temple University
• Keywords: multivariate analysis ; sparsity ; reduced-rank regression ; dimensionality reduction ; regularization ; graphical methods

Abstract

As enormous data sets become the norm rather than the exception, statistics as a scientific discipline is changing to keep up with this development. Of particular interest are regression problems in which attention to high dimensionality has become an important part in determining how to proceed. In multiple regression, regularization and sparsity considerations have led to new methodologies for dealing with the high-dimensionality, low sample-size situation. In multivariate regression, rank restrictions have led to a reduced-rank regression model that incorporates many of the classical dimensionality-reduction methodologies as special cases. In this talk, we discuss problems of working with regression data when there are a large number of variables and a relatively small number of observations, and we explore some new graphical ideas in the multivariate case.