title: Joint Estimation of Multiple Graphical Models from High Dimensional Time Series.
abstract: In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected fromnsubjects, each of which consists ofTpossibly 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 dimensiondcan increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and the 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.
authors.affiliation: Johns Hopkins University, Baltimore, USA.
authors.forename: Huitong
authors.initials: H
authors.lastname: Qiu
authors.affiliation: Johns Hopkins University, Baltimore, USA.
authors.forename: Fang
authors.initials: F
authors.lastname: Han
authors.affiliation: Princeton University, Princeton, USA.
authors.forename: Han
authors.initials: H
authors.lastname: Liu
authors.affiliation: Johns Hopkins University, Baltimore, USA.
authors.forename: Brian
authors.initials: B
authors.lastname: Caffo
keywords: Conditional independence; Graphical model; High dimensional data; Rate of convergence; Time series