Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors

Matrix and tensor completion are frameworks for a wide range of problems, including collaborative filtering, missing data, and image reconstruction. Missing entries are estimated by leveraging an assumption that the matrix or tensor is low-rank. Most existing Bayesian techniques encourage rank-sparsity by modelling factorized matrices and tensors with Normal-Gamma priors. However, the Horseshoe prior and other "global-local" formulations provide tuning-parameter-free solutions which may better achieve simultaneous rank-sparsity and missing-value recovery. We find these global-local priors outperform commonly used alternatives in simulations and in a collaborative filtering task predicting board game ratings.