Joint Estimation of Multiple Graphical Models from High Dimensional Time Series
This work addresses the challenge of modeling brain connectivity patterns from fMRI data for neuroscience applications, representing an incremental improvement in multi-subject graphical model estimation.
The authors tackled the problem of jointly estimating multiple graphical models from high-dimensional time series data, proposing a kernel-based method that leverages smooth variation across subjects and demonstrating its effectiveness on synthetic and real rs-fMRI data with theoretical convergence rates.
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.