Model Selection for High-Dimensional Data with Applications in Feature Selection and Network Building

• Activity Number: 320
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Xin Gao*+ and Peter Song and Yuehua Wu
• Companies: York University and University of Michigan and York University
• Keywords: composite likelihood ; variable selection ; Gaussian graphical model ; BIC ; model selection ; consistency

Abstract

For high-dimensional data set with complicated dependency structures, the full likelihood approach often leads to intractable computational complexity. This imposes difficulty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying marginal model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size. In this talk, we will also discuss the result that using a modified Bayesian information criterion (BIC) to select the tuning parameter in penalized likelihood estimation of Gaussian graphical model can lead to consistent network model selection even when $P$ increases with $N,$ as long as all the network edges are contained in a bounded subset.