  Graphical model has been widely used to investigate the complex dependence
structure of high-dimensional data, and it is common to assume that observed
data follow a homogeneous graphical model. However, observations usually come
from different resources and have heterogeneous hidden commonality in
real-world applications. Thus, it is of great importance to estimate
heterogeneous dependencies and discover subpopulation with certain commonality
across the whole population. In this work, we introduce a novel regularized
estimation scheme for learning nonparametric mixture of Gaussian graphical
models, which extends the methodology and applicability of Gaussian graphical
models and mixture models. We propose a unified penalized likelihood approach
to effectively estimate nonparametric functional parameters and heterogeneous
graphical parameters. We further design an efficient generalized effective EM
algorithm to address three significant challenges: high-dimensionality,
non-convexity, and label switching. Theoretically, we study both the
algorithmic convergence of our proposed algorithm and the asymptotic properties
of our proposed estimators. Numerically, we demonstrate the performance of our
method in simulation studies and a real application to estimate human brain
functional connectivity from ADHD imaging data, where two heterogeneous
conditional dependencies are explained through profiling demographic variables
and supported by existing scientific findings.
