Fall 2015 Seminar Series

DATE: 9/24/15
LOCATION: E51-315
TIME: 4:15pm
Reception immediately following

SPEAKER:
Martin Copenhaver

TITLE
The Role of Robustness in Modern Statistical Regression

ABSTRACT
From linear regression via the Lasso to matrix completion and beyond, sparsity is a key driver in modern statistical problems. In stark contrast to sparsity motivations for such problems, it is known in the field of robust optimization that a variety of vector regression problems, such as Lasso, can arise by simply immunizing a nominal problem to uncertainty in the data. Such a robustification offers an explanation for why some linear regression methods perform well in the face of noise, even when these methods do not reliably produce sparse solutions. In this talk, we explore and deepen the understanding of the role that robustness plays in popular regularization methods. With regularized least squares, Lasso, and matrix completion as motivating examples, we characterize precisely when regularization problems correspond to simple robust optimization problems. In doing so, we contend that it is robustness, not sparsity, which is critical to the success of modern statistical methods.

Joint work with Dimitris Bertsimas.