Mixture of Functional Graphical Models with an Application to ADHD Data

• Activity Number: 481 - Nonparametric Methods in Functional Data Analysis
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Qihai Liu* and Lucas Price and Kevin Lee and Hyun Bin Kang
• Companies: Western Michigan University and AeroVironment and Western Michigan University and Western Michigan University
• Keywords: Functional graphical models; Mixture models; EM algorithm; Graphical lasso; Attention deficit hyperactivity disorder (ADHD)

Abstract

Graphical models have been widely used to investigate the complex dependence structure of high-dimensional data. Recently there has been an interest to apply graphical model to functional data to understand the conditional dependence structure among random functions. In the current literature, it is common to assume that the data come from a homogeneous resource, but the observed data from real world often come from different resources and may have heterogeneous dependencies across the whole population. In this presentation, we propose a mixture of functional graphical models, where the random functions are from a mixture of Gaussian processes with different conditional dependence structures. We propose the scheme of detecting heterogeneous groups and recovering dependency structures through functional graphical lasso and EM algorithm. Numerically we demonstrate the performance of our method through simulation studies and an application to the attention deficit hyperactivity disorder (ADHD) data that consist of rs-fMRI scans for each subject.