A Local Approach to Estimation in Discrete Loglinear Models

• Activity Number: 626
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Statistical and Applied Mathematical Sciences Institute
• Author(s): Helene M. Massam* and Nanwei Wang
• Companies: York University and York University
• Keywords: discrete ; graphical models ; distributed ; maximum likelihood ; marginal

Abstract

We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. Fienberg and Rinaldo (2012) have shown that the mle does not exists iff the data vector belongs to a face of the marginal cone spanned by the rows of the design matrix of the model. Identifying these faces in high-dimension is challenging. In this paper, we take a local approach: We show that one such face, albeit possibly not the smallest one, can be identified by looking at a collection of marginal graphical models generated by induced subgraphs. Our second contribution concerns the composite maximum likelihood estimate. We show that the estimate is the same whether we use local conditional or marginal likelihoods. We also study its asymptotic behaviour when both the dimension of the model and the sample size are large.