5ef0b4eba35ab2d6180b0bca7e46b6f9-Reviews.html

SUMMARY This paper studies the problem of low rank matrix completion which exists in many real-world applications such as collaborative filtering for recommender systems. A previous work (ref [4]) proposed a scalable algorithm called Soft-Impute for solving a convex optimization problem involving the nuclear norm as a regularizer. Like previous work such as probabilistic matrix factorization (PMF), this paper gives the problem a probabilistic interpretation by relating the (non-probabilistic) optimization problem to a MAP estimation problem. Different (concave) penalty functions of the nuclear norm are proposed and then an EM algorithm is proposed to solve the MAP estimation problem. The algorithms proposed in this paper are more general than the Soft-Impute algorithm proposed in [4] in that the latter comes as a particular case.