Near-Neighbor Methods in Random Preference Completion

Abstract This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with n agents (users) {xi}i∈[n] and m alternatives (items) {yl}l∈[m], each of which is associated with a latent feature vector. Agents rank items nondeterministically according to the Plackett-Luce model, where the higher the utility of an item to the agent, the more likely this item will be ranked high by the agent. Our goal is to identify near neighbors of an arbitrary agent in the latent space for prediction.We first show that the Kendall-tau distance based kNN produces incorrect results in our model. Next, we propose a new anchor-based algorithm to find neighbors of an agent. A salient feature of our algorithm is that it leverages the rankings of many other agents (the so-called “anchors”) to determine the closeness/similarities of two agents. We provide a rigorous analysis for one-dimensional latent space, and complement the theoretical results with experiments on synthetic and real datasets. The experiments confirm that the new algorithm is robust and practical.