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Abstract:
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We propose a Bayesian low-rank graph regression modeling (BLGRM) framework for the regression analysis of matrix response data. This development is motivated by performing detailed comparisons of functional and structural connectivity data across subjects, groups, and time and relating connections to particular behavioral measures. The BLGRM can be regarded as a novel integration of principal component analysis, tensor decomposition, and regression models. In BLGRM, we find a common low-dimensional subspace for efficiently representing all matrix responses. Based on such low-dimensional representation, we can easily quantify the effects of predictors of interest, such as diagnosis status, and then perform regression analysis in the common subspace, leading to both substantial dimension reduction and much better prediction. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BLGRM and its comparison with competing approaches. We apply BLGRM to the rest functional magnetic resonance imaging (rfMRI) data obtained from the Alzheimer's disease Neuroimaging Initiative (ADNI).
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