Title: High dimensional covariance selection for multiple graphical models under structured sparsity
Advisor: Professor George Michaidilis
Committee Members: Professor Xuming He, Professor Kerby Shedden, Professor Ji Zhu
Abstract: Gaussian graphical models capture the dependence relationships between random variables through the pattern of nonzero elements in the corresponding inverse covariance matrices. There has been a lot of work in the literature on the estimation problem of a single graphical model. However, in a number of application domains one has to estimate several related graphical models. We develop methodology that addresses this problem, assuming that the grouping pattern of the underlying models is known. The method consists of two steps. In the first one, we employ neighborhood selection to obtain approximate estimates for the structured sparsity pattern using a group lasso penalty. In the second step, we estimate the nonzero entries in the inverse covariance matrices based on the constraints from the previous step. We prove that the proposed estimator is consistent asymptotically for sparse high-dimensional graphical models under certain conditions.