Title: A Tour Through Gaussian Copula Graphical Models
Abstract: The hallmarks of modern datasets are their imposing sizes, intricate dependence structures and non-Gaussian behaviors. High dimensional graphical modeling is one specific topic where all three of these issues intertwine. As such, one needs to bring together a large number of disparate tools to understand and analyze such problems. In this talk, I will describe high dimensional sparsely connected Gaussian copula graphical models and advances that have been made in understanding them. Estimation of these graphs are carried out via non-parametric measures of associations namely, Kendall’s tau and Spearman’s rho. Regularization strategies that tackle the high dimensionality issue, will be discussed. We will talk about testing for the presence of edges in these graphs. In particular, a regularized score test approach will be discussed. We will also show how these score tests can be used to estimate the graph with control of false discovery rate in a multiple testing framework. We will finish by introducing a new directional likelihood method that can be used to do chi-squared type goodness-of-fit tests for graphs when a pre-specified sparsity sub-structure needs to be statistically ratified.