Is Sparseness the Answer to Model Selection as Well as Prediction?

• Activity Number: 380
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Peter J. Bickel*+ and Ya'akov Ritov
• Companies: University of California at Berkeley and Hebrew University
• Keywords: nonparametric regression ; model selection ; Lasso

Abstract

There has been considerable emphasis on thresholding and the LASSO as computable methods leading to sharp Oracle bounds and optimal prediction rates with high dimensional covariates in regression and more generally(Buhlmann,Meinshausen,Yu,Candes,Tao,Ritov,Tsybakov and many others). These results are predicated on the existence of unique sparsest representations of the regression. There has been considerable extension of these inquiries into identifying the variables entering into such representations of the regression.,or equivalently model building under the same conditions as those used in prediction(Wainwright and others). We argue that in many situations, for instance biological network identification ,there are many optimal predictors involving quite different combinations of variables. We present serious failures of the Lasso in such situations and discuss some alternative approaches