Finite mixtures of functional graphical models: Uncovering heterogeneous dependencies in high-dimensional data.

Graphical models have been widely used to explicitly capture the statistical relationships among the variables of interest in the form of a graph. The central question in these models is to infer significant conditional dependencies or independencies from high-dimensional data. In the current literature, it is common to assume that the high-dimensional data come from a homogeneous source and follow a parametric graphical model. However, in real-world context the observed data often come from different sources and may have heterogeneous dependencies across the whole population. In addition, for time-dependent data, many work has been done to estimate discrete correlation structures at each time point but less work has been done to estimate global correlation structures over all time points. In this work, we propose finite mixtures of functional graphical models (MFGM), which detect the heterogeneous subgroups of the population and estimate single graph for each subgroup by considering the correlation structures. We further design an estimation method for MFGM using an iterative Expectation-Maximization (EM) algorithm and functional graphical lasso (fglasso). Numerically, we demonstrate the performance of our method in simulation studies and apply our method to high-dimensional electroencephalogram (EEG) dataset taken from an alcoholism study.