B1210
Title: Joint estimation of heterogeneous non-Gaussian functional graphical models with fully and partially observed curves
Authors: Eftychia Solea - Queen Mary University of London (United Kingdom) [presenting]
Abstract: We introduce a new methodology for estimating undirected graphical models for heterogeneous non-Gaussian multivariate functional data, such as brain activities collected by functional magnetic resonance imaging from a sample of subjects with different subtypes of a neurological disease. The goal of the new model is to estimate robustly a collection of functional graphical models, corresponding to several subpopulations that share some common dependence structure. The model is fitted via a joint estimation method employed with the hierarchical penalty that encourages a common graph structure and individual sparsity. To relax the Gaussian assumption, we consider the functional Gaussian copula graphical model, and propose the rank-based Kendall's tau correlation operator that extends the Kendall's tau correlation coefficient to the functional setting. We establish the concentration inequalities of the estimates and the graph selection consistency for both completely and partially observed data, while allowing the number of functions to diverge to infinity with the sample size. We demonstrate the efficiency of our method through both simulations and an analysis of the fMRI ADHD-200 data set of subjects with inattentive and combined subtypes of ADHD, and control subjects
