Student Seminars

Jing Ma
PhD student, Department of Statistics, University of Michigan

Estimating Multiple Graphical Models with Structures

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 structural relationships of the underlying graphs are known. The method consists of two steps. In the first one, we employ neighborhood selection to obtain estimates of the structured sparsity pattern using a group lasso penalty. In the second step, we estimate the nonzero entries in the inverse covariance matrices using maximum likelihood. We prove that the proposed estimator is consistent asymptotically for sparse high-dimensional graphs under certain conditions and illustrate its performance using simulated experiments as well as a climate data set.

Student Seminar Archive

For questions regarding the Statistics Student Seminar or if you are interested in presenting, please contact Joonha Park(joonhap@umich.edu) or Jingshen Wang(jshwang@umich.edu).