Penalized and Constrained Regression
Presented by Gareth James, University of Southern California
Thursday, May 21, 2015
Time: 10:30 AM – 12:00 PM Pacific / 1:30 PM – 3:00 PM Eastern
Host Location: Santa Monica, conference room 5401
Other Locations: Pittsburgh (room 6208) & Washington, DC (room 7401)
Motivated by applications in areas as diverse as finance, marketing, image reconstruction, and curve estimation, we consider the constrained high-dimensional generalized linear model (GLM) problem, where the underlying parameters satisfy a collection of linear constraints. We develop the Penalized and Constrained regression method (PAC) for computing the penalized coefficient paths on high-dimensional GLM fits, subject to a set of linear constraints. PAC is an extremely general method which encompasses many statistical approaches, such as the fused lasso, monotone curve estimation and the generalized lasso. Computing the PAC coefficient path poses some technical challenges but we develop an efficient algorithm for fitting the path over a grid of tuning parameters. We provide non-asymptotic error bounds which suggest that PAC should outperform unconstrained penalized GLM methods in situations where the true parameters satisfy the underlying constraints. Finally, our empirical results show that PAC performs well, both computationally and statistically.
About the Presenter
Professor Gareth James received his Ph.D. in Statistics from Stanford University in 1998. He is Vice Dean for Faculty and Academic Affairs and the E. Morgan Stanley Chair in Business Administration in the Department of Data Sciences and Operations at the University of Southern California. Professor James’ main areas of statistical expertise involve functional data and high dimensional statistics. He is a Fellow of the American Statistical Association and has won several recent research and teaching awards, including two Deans Awards for Research Excellence, two Golden Apple awards, the Evan C. Thompson Faculty Teaching and Learning Innovation Award and the USC Mellon Mentoring Award.
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