Bayesian Tensor Binary Regression

In this paper we present a binary regression model with tensor coefficients and present a Bayesian model for inference, able to recover different levels of sparsity of the tensor coefficient. We exploit the CONDECOMP/PARAFAC (CP) representation for the tensor of coefficients in order to reduce the number of parameters and adopt a suitable hierarchical shrinkage prior for inducing sparsity. We propose a MCMC procedure with data augmentation for carrying out the estimation and test the performance of the sampler in small simulated examples.