Joint estimation of multiple graphical models from high dimensional time series

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 an explicit rate of convergence in parameter estimation. It characterizes the strength that one can borrow across different individuals and the effect of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging data illustrate the effectiveness of the method proposed.