Predictive Matrix-Variate T Models

Abstract

It is becoming increasingly important to learn from a partially-observed random matrix and predict its missing elements. We assume that the entire matrix is a single sample drawn from a matrix-variate t distribution and suggest a matrix-variate t model (MVTM) to predict those missing elements. We show that MVTM generalizes a range of known probabilistic models, and automatically performs model selection to encourage sparse predictive models. Due to the non-conjugacy of its prior, it is difficult to make predictions by computing the mode or mean of the posterior distribution. We suggest an optimization method that sequentially minimizes a convex upper-bound of the log-likelihood, which is very efficient and scalable. The experiments on a toy data and EachMovie dataset show a good predictive accuracy of the model.