Algebraic-Combinatorial Methods for Low-Rank Matrix Completion with Application to Athletic Performance Prediction

This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing entries in the general low rank setting. For positive data, we achieve results outperforming the state of the art nuclear norm, both in accuracy and computational efficiency, in simulations and in the task of predicting athletic performance from partially observed data.