Statistics and Data Science Seminar
Prof. Xin Gao
York University
Parameter Estimation and Model Selection in Graphical Models
Abstract: The recent years have witnessed the increasing interest in the study of graphical models. In this talk, I will discuss two related parameter estimation and model selection problems in graphical models. The first problem is to estimate the concentration matrix of a Gaussian graphical model. We propose to estimate the concentration matrix using the penalized likelihood method with the smoothly clipped absolute deviation (SCAD) penalty. The method leads to a sparse and shrinkage estimator of the concentration matrix. Using proper choice of the regularization parameter, the proposed method automatically and consistently selects the true graphical structure and produces estimator that is as efficient as the oracle estimator. We further establish the consistency of the BIC criterion to identify the true graphical structure when used with the SCAD penalty function. The second problem is regarding the graphic model with multivariate hidden Markov structure. For such high-dimensional data with complicated dependency structure, we propose to use composite likelihood approach and especially we develop COMP-EM algorithm to perform the parameter estimation in the presence of incomplete data. The composite likelihood based information criterion was employed to select the best network structure.
Wednesday April 23, 2008 at 3:30 PM in SEO 712