Title: Bayesian generalized sparse symmetric tensor-on-vector regression
Authors: Rajarshi Guhaniyogi - University of California Santa Cruz (United States) [presenting]
Abstract: Motivated by brain connectome datasets acquired from various imaging modalities, a novel generalized Bayesian linear modeling framework with a symmetric tensor response and scalar predictors is proposed. The symmetric tensor coefficients corresponding to the scalar predictors are embedded with two features: low-rankness and group sparsity within the low-rank structure. Besides offering computational efficiency and parsimony, these two features enable identification of important tensor nodes and tensor cells significantly associated with the predictors. We establish that the posterior predictive density from the proposed model is close to the true density, the closeness being measured by the Hellinger distance between these two densities, which scales at a rate nearing the finite dimensional optimal rate of square root of the sample size, depending on how the number of tensor nodes grows with the sample size. The proposed framework is empirically investigated under various simulation settings and with a brain connectome dataset.