Abstract

 We introduce the framework of blind regression motivated by matrix completion for recommendation systems: given m users, n movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of nonparametric statistics, we posit that user u and movie i have features x1 (u) and x2 (i) respectively, and their corresponding rating y(u, i) is a noisy measurement of  for some unknown function f . In contrast with classical regression, the features  are not observed, making it challenging to apply standard regression methods to predict the unobserved ratings.