Grouping Pursuit and Feature Selection Over a Graph

• Activity Number: 189
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yunzhang Zhu*+ and Xiaotong Shen
• Companies: University of Minnesota and University of Minnesota
• Keywords: Gene networks ; large p but small n ; nonconvex regularizer ; supervised clustering

Abstract

Low-dimensional structures such as sparseness or homogenous subgroups of predictors are useful in high-dimensional regression analysis. In this article, we identify the grouping structure with respect to the size of regression coefficients, while achieving sparseness of a model, where predictors correspond to nodes over an undirected graph representing prior knowledge about grouping, and edges for two connecting nodes indicate that grouping is likely between them. This is motivated from gene networks, where genes tend to work in groups according to their biological functionalities. Through the method of non-convex regularization, we develop computational tools and study theoretical result for the proposed method. Both simulation studies and theoretical results show that the true underlying model can be recovered through our method. An application to gene network data will be discussed.