Group-Regularized Estimation Under Strong Hierarchy

• Activity Number: 275
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): He Jiang*+ and Yiyuan She
• Companies: Florida State University and Florida State University
• Keywords: Interaction effect ; Strong hierarchy ; Group multi-regularization ; Minimax optimal rate

Abstract

In many high-dimensional models involving interaction effects, statisticians usually favor variable selection obeying certain logical hierarchical constraints. The talk focuses on strong hierarchy which means that the existence of an interaction term implies that both associated main effects must be present. Although lately the hierarchical lasso has been proposed, the existing computational algorithms converge quite slow and cannot meet the challenge of big data. More importantly, the literature of finite-sample studies is extremely scarce, largely due to the difficulty that multiple sparsity-promoting penalties are enforced on the same subject. A new type estimators based on group multi-regularization is investigated to capture various types of structural parsimony simultaneously. We present some nonasymptotic results, reveal the minimax optimal rates, and develop a general-purpose algorithm with a theoretical guarantee of strict iterate convergence. Some simulations and real data examples are shown to demonstrate the efficiency and efficacy of the proposed method.