Skip to content


General Contact Information

 

Phone: 646-660-6500

Fax: 646-660-6501

 

Email:

provost.office@baruch.cuny.edu

 

Mailing Address:

Office of the Provost & Senior Vice President for Academic Affairs

Baruch College/CUNY

One Bernard Baruch Way
Box D-701

New York, NY 10010-5585

 

Walk-In Address:

Administrative Center

135 East 22nd Street, 7th Floor

Office of the Provost and Senior Vice President for Academic Affairs

Message Archive



Monday, November 27, 2017

 

This email is being sent to all members of the Baruch College faculty.

For an archive of announcements sent from the Associate Provost beginning June 2011, click here.

 

The Information Systems and Statistics Research Seminar Series

Presented by the Paul H. Chook Department of Information Systems and Statistics

How to generalize bias and variance to convex regularized estimators?

Pierre Bellec, Assistant Professor, Rutgers University

Thursday, November 30, 12:30-1:45pm
NVC 11-217, ISS Conference Room

 

From: Prof. Rongning Wu, Paul H. Chook Department of Information Systems and Statistics

Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. However, there are still simple open questions about these estimators, even in the simple linear regression model. We are particularly interested in the following open questions:


1)    The bias and variance of linear estimators are easy to define and provide precise insights on the performance of linear estimators. How can bias and variance be generalized to nonlinear convex estimators?
2)    The performance guarantees of these estimators require the tuning parameter to be larger than some universal threshold, but the literature is mostly silent about what happens if the tuning parameter is smaller than this universal threshold. How bad is the performance when the tuning parameter is below the universal threshold?
3)    The correlations in the design can significantly deteriorate the empirical performance of these nonlinear estimators. Is it possible to quantify this deterioration explicitly? Is there a price to pay for correlations; in particular, is the performance for correlated designs always worse than that for orthogonal designs?
4)    Most theoretical results on the Lasso and its variants rely on conditions on the design matrix. These conditions greatly simplify the proofs and our understanding of these estimators, but it is still unclear whether these conditions are truly necessary of whether they are an artifact of the proofs. Are these conditions actually necessary?

We will provide some general properties of norm-penalized estimators and propose a generalization of the bias and the variance for these nonlinear estimators. These generalizations of bias/variance will hopefully let us answer the above questions.

 

Rongning Wu

Paul H. Chook Department of Information Systems and Statistics