Nonparametric Preference Completion
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We consider the task of collaborative preference completion: given a pool of items, a pool of users and a partially observed item-user rating matrix, the goal is to recover the personalized ranking of each user over all of the items. Our approach is nonparametric: we assume that each item i and each user u have unobserved features x_i and y_u, and that the associated rating is given by g_u(f(x_i,y_u)) where f is Lipschitz and g_u is a monotonic transformation that depends on the user. We propose a k-nearest neighbors-like algorithm and prove that it is consistent. To the best of our knowledge, this is the first consistency result for the collaborative preference completion problem in a nonparametric setting. Finally, we conduct experiments on the Netflix and Movielens datasets that suggest that our algorithm has some advantages over existing neighborhood-based methods and that its performance is comparable to some state-of-the art matrix factorization methods.
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