Interpretable Matrix Completion: A Discrete Optimization Approach

We consider the problem of matrix completion with side information on an $n\times m$ matrix. We formulate the problem exactly as a sparse regression problem of selecting features and show that it can be reformulated as a binary convex optimization problem. We design OptComplete, based on a novel concept of stochastic cutting planes to enable efficient scaling of the algorithm up to matrices of sizes $n = 10^6$ and $m = 10^5$. We report experiments on both synthetic and real-world datasets that show that OptComplete outperforms current state-of-the-art methods both in terms of accuracy and scalability, while providing insight on the factors that affect the ratings.