Joint Graphical Lasso with Regularized Aggregation

Music City Center 

We present methods for estimating multiple precision matrices for high-dimensional time series within the framework of Gaussian graphical models, with a specific focus on analyzing functional magnetic resonance imaging (fMRI) data collected from multiple subjects. Our goal is to estimate both individual brain networks and a collective structure representing a group of subjects. To achieve this, we propose a method that utilizes group Graphical Lasso and regularized aggregation to simultaneously estimate individual and group precision matrices, assigning varying weights to each individual based on their outlier status within the group. We investigate the convergence rates of the precision matrix estimators across different norms and expectations, assessing their performance under both sub-Gaussian and heavy-tailed assumptions. The effectiveness of our methods is demonstrated through simulations and real fMRI data analysis.

Aggregation

Brain connectivity

Joint estimation

Precision matrix estimation

Regularization

Long-memory 

Korean International Statistical Society