Maximum likelihood inference for a large precision matrix

• Activity Number: 549 - Recent Development of Statistical Learning Methods for Complex Biomedical Data
• Type: Invited
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Yunzhang Zhu and Xiaotong T Shen* and Wei Pan
• Companies: Ohio State University and University of Minnesota and University of Minnesota
• Keywords: High-dimensional inference ; Graphical models ; Regularization

Abstract

Inference concerning Gaussian graphical models involves pairwise conditional dependencies on Gaussian random variables. In such a situation, regularization of a certain form is often employed to treat an overparameterized model, imposing challenges to inference. In this talk, we will present a constrained maximum likelihood method for inference, with a focus of alleviating the impact of regularization on inference. For general composite hypotheses, we unregularize hypothesized parameters whereas regularizing nuisance parameters through a L0-constraint controlling the degree of sparseness. For the likelihood ratio test, the corresponding distribution is the chi-square or normal, depending on if the co-dimension of a test is finite or increases with the sample size. This goes beyond the classical Wilks phenomenon. Some numerical results will be discussed, in additional to an application to network analysis.