Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Helen Zhang
North Carolina State University
"Soft-thresholding Penalties for Variable Selection"
ABSTRACT
We present two new types of shrinkage and selection operators for variable selection, one in linear regression context and the other for nonparametric regression models. For linear models, a new LASSO-type penalty equipped with adaptive weights is introduced. Theoretical properties, including consistency and oracle properties, and the computational algorithm of the estimator are discussed. For nonparametric regression models, we introduce a new regularization method ``COSSO'' for simultaneous function smoothing and component selection. In the framework of smoothing spline ANOVA models, the ``COSSO'' applies a novel soft thresholding operation to function components with the sum of RKHS norms as a penalty form. Theoretical properties of the COSSO are presented. We also discuss the Bayesian perspectives for these methods and suggest the possible Bayesian formulation and related open questions.
Tuesday, November, 28, 2006
4:00 - 5:00 pm
208 Patterson Hall