Direct Estimation of differential networks under high-dimensional nonparanormal graphical models

In genomics, it is often of interest to study the structural change of a genetic network between two phenotypes. Under Gaussian graphical models, the problem can be transformed to estimating the difference between two precision matrices, and several approaches have been recently developed for this task such as joint graphical lasso and fused graphical lasso. However, the multivariate Gaussian assumptions made in the existing approaches are often violated in reality. In this talk, I will consider the problem of directly estimating differential networks under a flexible semiparametric model, namely the nonparanormal graphical model, where the random variables are assumed to follow a multivariate Gaussian distribution after a set of monotonically increasing transformations. I will introduce a novel rank-based estimator to directly estimate the differential network, together with a parametric simplex algorithm for fast implementation. I will show that the proposed estimator is consistent in both parameter estimation and support recovery under a high-dimensional setting where p grows with n almost exponentially fast.

Dr. Zhang is an Assistant Professor in the department of mathematical science at the University of Arkansas. His research interests include Bayesian network inference and its application to system biology. He holds a Bachelor of science in statistics from Beijing Normal University and Ph.D in statistics from Northwestern University.