  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.
