2025/05/20 by Shao-Hsuan Wang, Wang, Shao-Hsuan, Hsin-Hsiung Huang +1
Mathematics · #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2505.13821
Ultra-high-dimensional tensor predictors are increasingly common in neuroimaging and other biomedical studies, yet existing methods rarely integrate continuous, count, and binary responses in a single coherent model. We present a Bayesian Sparse Kronecker Product Decomposition (BSKPD) that represents each regression (or classification) coefficient tensor as a low-rank Kronecker product whose factors are endowed with element-wise Three-Parameter Beta-Normal shrinkage priors, yielding voxel-level sparsity and interpretability. Embedding Gaussian, Poisson, and Bernoulli outcomes in a unified exponential-family form, and combining the shrinkage priors with Polya-Gamma data augmentation, gives closed-form Gibbs updates that scale to full-resolution 3-D images. We prove posterior consistency and identifiability even when each tensor mode dimension grows subexponentially with the sample size, thereby extending high-dimensional Bayesian theory to mixed-type multivariate responses. Simulations and applications to ADNI and OASIS magnetic-resonance imaging datasets show that BSKPD delivers sharper signal recovery and lower predictive error than current low-rank or sparsity-only competitors while preserving scientific interpretability.