Matrix Factorization at the Frontier of Non-convex Optimizations

Abstract

Principal Component Analysis (PCA) and Canonical Component Analysis (CCA) are two of the few examples of non-convex optimization problems that can be solved efficiently with sharp guarantees. This is achieved by the classical and well-established understanding of matrix factorizations. Recently, several new theoretical and algorithmic challenges have arisen in statistical learning over matrix factorizations, motivated by various real-world applications. Despite the inherent non-convex nature of these problem, efficient algorithms are being discovered with provable guarantees, extending the frontier of our understanding of non-convex optimization problems. I will present several recent results in this area in applications to matrix completion and sensing, crowdsourcing, ranking, and tensor factorization.