Distributed Matrix Completion

We discuss parallel and distributed algorithms for large-scale matrix completion on problems with millions of rows, millions of columns, and billions of revealed entries. We focus on in-memory algorithms that run on a small cluster of commodity nodes, even very large problems can be handled effectively in such a setup. Our DALS, ASGD, and DSGD++ algorithms are novel variants of the popular alternating least squares and stochastic gradient descent algorithms, they exploit thread-level parallelism, in-memory processing, and asynchronous communication. We provide some guidance on the asymptotic performance of each algorithm and investigate the performance of both our algorithms and previously proposed Map Reduce algorithms in large-scale experiments. We found that DSGD++ outperforms competing methods in terms of overall runtime, memory consumption, and scalability. Using DSGD++, we can factor a matrix with 10B entries on 16 compute nodes in around 40 minutes.