Date & Time: Monday, January 18, 2010 12:30-13:15.
Venue: Ramanujan Hall
Title: Shrinkage estimation in the Lasso set up
Speaker: Rajendran Narayanan, Cornell University
Abstract: It is well-known that James-Stein type estimators dominate the MLE of the mean of a multivariate normal distribution when the dimension exceeds three. We consider the problem of improving the Lasso or l1 penalised regression. Lasso solution can be shown to be the projection of the OLS estimator. Treating the Lasso estimator as the restricted MLE of the regression parameters, we shrink the OLS vector to a closed convex set, precisely, a p-dimensional crosspolytope whose size is parameterised by a tuning parameter. Considering shrinkage estimation in this geometric framework, we construct a class of estimators exhibiting risk gains over Lasso with comparable prediction risk estimates. This in turn also enables a data based method of choosing the tuning parameter. Borrowing from principles of convexity theory, we propose a theoretical basis to ensure model sparsity.