Collaborative Filtering via Rating Concentration

While most popular collaborative filtering methods use low-rank matrix factorization and parametric density assumptions, this article proposes an approach based on distribution-free concentration inequalities. Using agnostic hierarchical sampling assumptions, functions of observed ratings are provably close to their expectations over query ratings, on average. A joint probability distribution over queries of interest is estimated using maximum entropy regularization. The distribution resides in a convex hull of allowable candidate distributions which satisfy concentration inequalities that stem from the sampling assumptions. The method accurately estimates rating distributions on synthetic and real data and is competitive with low rank and parametric methods which make more aggressive assumptions about the problem.