Low rank matrix completion via random sampling

In this work, we present a method to find a low rank approximation to a large matrix with missing entries. Optimization methods, EM based methods or Variational Bayesian methods are proposed to solve this problem. However, the computational cost of these methods can be prohibitively large in case of a massive data matrix, when the known entries do not even fit into the fast random access memory (RAM). Traditional methods access the data matrix several times during iterations and the data transfer from a secondary storage becomes the key bottleneck. To alleviate this problem, we devise a randomized scheme by sampling a subset of rows or columns of the original matrix. The resulting algorithm is efficient in terms of the number of required disk accesses, is highly parallelizable and produces factorizations that are competitively accurate.