Nonparametric Preference Completion

TL;DR

This paper introduces a nonparametric method for collaborative preference completion, using a k-nearest neighbors approach, and proves its consistency, with experiments on real datasets demonstrating its effectiveness.

Contribution

It presents the first consistency proof for a nonparametric collaborative preference completion algorithm and introduces a k-nearest neighbors-like method for the task.

Findings

Algorithm is consistent in the nonparametric setting.

Effective performance demonstrated on Netflix and Movielens datasets.

First known consistency result for this problem in a nonparametric framework.

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.