This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting in poor estimation and predictive performance. We develop a novel class of multiway shrinkage priors for the coefficients in tensor regression models. Properties are described, including posterior consistency under mild conditions, and an efficient Markov chain Monte Carlo algorithm is developed for posterior computation. Simulation studies illustrate substantial gains over vectorizing or using existing tensor regression methods in terms of estimation and parameter inference. The approach is further illustrated in a neuroimaging application.
The recent paper Bayesian Tensor Regression REF develops a model for regression with scalar responses and tensor covariates.
Bayesian Tensor Regression
arXiv: Methodology
Mathematics Computer Science