Thy Friend is My Friend: Iterative Collaborative Filtering for Sparse Matrix Estimation

The sparse matrix estimation problem consists of estimating the distribution of an n n matrix Y, from a sparsely observed single instance of this matrix where the entries of Y are independent random variables. This captures a wide array of problems; special instances include matrix completion in the context of recommendation systems, graphon estimation, and community detection in (mixed membership) stochastic block models. Inspired by classical collaborative filtering for recommendation systems, we propose a novel iterative, collaborative filteringstyle algorithm for matrix estimation in this generic setting.