Please Note: This seminar will be given online.
Estimating Time-varying Brain Connectivity
The human brain is a complex dynamical system composed of many interacting regions. Knowledge of these interactions is the cornerstone for understanding the brain functional architecture and the relationship between neural dynamics. Brain connectivity can be represented as a network composed of a set of random variables (nodes) interconnected by a set of interactions (edges). As the brain is actively yielding thoughts and ideas, along with changes in arousal, awareness, and vigilance, modelling brain connectivity as a static network where a single snapshot of the network is observed can be misleading. We study time-varying networks and model the brain data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time point be sparse, but also that precision matrices at neighboring time points be similar. We accomplish this by generalizing the Elastic Net of Zou and Hastie (2005) and the Fused LASSO of Tibshirani et al. (2005), and solving the resulting optimization problems with an efficient ADMM-based algorithm that utilizes blockwise fast computation. This is joint work with Dr. Peijun Sang and Dr. Mu Zhu.