In this manuscript the problem of jointly estimating multiple graphical models in high dimensions is considered. It is assumed that the data are collected from n subjects, each of which consists of m non-independent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of the closeness between subjects. A kernel based method for jointly estimating all graphical models is proposed. Theoretically, under a double asymptotic framework, where both (m,n) and the dimension d can increase, the explicit rate of convergence in parameter estimation is provided, thus characterizing 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.
Multivariate Analysis | Statistical Methodology
Qiu, Huitong; Han, Fang; Liu, Han; and Caffo, Brian, "Joint Estimation of Multiple Graphical Models from High Dimensional Time Series" (November 2013). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 259.