In this manuscript we consider the problem of jointly estimating multiple
graphical models in high dimensions. We assume that the data are collected from
n subjects, each of which consists of T possibly dependent observations. The
graphical models of subjects vary, but are assumed to change smoothly
corresponding to a measure of closeness between subjects. We propose a kernel
based method for jointly estimating all graphical models. Theoretically, under
a double asymptotic framework, where both (T,n) and the dimension d can
increase, we provide the explicit rate of convergence in parameter estimation.
It characterizes the strength one can borrow across different individuals and
impact of data dependence on parameter estimation. Empirically, experiments on
both synthetic and real resting state functional magnetic resonance imaging
(rs-fMRI) data illustrate the effectiveness of the proposed method.Comment: 40 page
