Simultaneous Grouping Pursuit and Feature Selection Over an Undirected Graph

• Activity Number: 63
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yunzhang Zhu and Xiaotong Shen and Wei Pan
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: statistical learning ; Network analysis ; structured data ; non-convex minimization ; prediction

Abstract

In high-dimensional regression, grouping pursuit and feature selection have their own merits while complementing each other in battling the curse of dimensionality. To seek a sparse model, we perform simultaneous grouping pursuit and feature selection over an undirected graph with each node corresponding to one predictor. When the corresponding nodes are connected over the graph, regression coefficients can be grouped, whose absolute values are the same or close. This is motivated from gene network analysis, where genes tend to work in groups according to their biological functionalities. Through a non-convex method, we develop a computational method and analyze the proposed method. Theoretical analysis indicates that the proposed method reconstructs the oracle estimator--the unbiased least squares estimator given the true grouping, leading to consistent reconstruction of grouping structures and informative features, as well as to optimal parameter estimation. Simulation studies suggest that the method combines the benefit of both grouping pursuit and feature selection, and compares favorably against its competitors in accuracy of selection and predictive performance.