  In this study we focus on the problem of joint learning of multiple
differential networks with function Magnetic Resonance Imaging (fMRI) data sets
from multiple research centers. As the research centers may use different
scanners and imaging parameters, joint learning of differential networks with
fMRI data from different centers may reflect the underlying mechanism of
neurological diseases from different perspectives while capturing the common
structures. We transform the task as a penalized logistic regression problem,
and exploit sparse group Minimax Concave Penalty (gMCP) to induce common
structures among multiple differential networks and the sparse structures of
each differential network. To further enhance the empirical performance, we
develop an ensemble-learning procedure. We conduct thorough simulation study to
assess the finite-sample performance of the proposed method and compare with
state-of-the-art alternatives. We apply the proposed method to analyze fMRI
datasets related with Attention Deficit Hyperactivity Disorder from various
research centers. The identified common hub nodes and differential interaction
patterns coincides with the existing experimental studies.
