Title: Nonparametric Preference Completion,
Abstract: 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 \emph{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
demonstrate the performance of our algorithm with experiments on the Netflix
and Movielens datasets.