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Abstract
In the Gaussian graphical model framework, precision matrices reveal conditional dependence structure among random variables. In functional magnetic resonance imaging (fMRI) data, estimating such precision matrices of multi-subjects and aggregating them to a group-level is an essential step for constructing a group brain network. In this dissertation, I consider joint estimation of multiple precision matrices with regularized aggregation under both Gaussian and Non-Gaussian assumptions. In the estimation of individual precision matrices, I take a regularization approach to induce sparsity, which makes brain network estimation more realistic. Also, in the construction of a group precision matrix, the simple average of individual precision matrices may be affected by outliers and provide inconsistent outcomes between subject-level and group-level networks. In contrast, the proposed methods yield a robust group graph which can identify and ease the effect of outliers. I demonstrate the effectiveness of the proposed methods through simulated examples and analyses on saccade tasks fMRI data.