Preference Completion: Large-scale Collaborative Ranking from Pairwise Comparisons

TL;DR

This paper introduces a scalable collaborative ranking method from pairwise preferences, providing theoretical guarantees and a practical large-scale algorithm that outperforms existing baselines in ranking tasks.

Contribution

It offers a convex optimization approach with strong generalization guarantees and develops AltSVM, a scalable non-convex algorithm based on alternating minimization for large datasets.

Findings

Convex method achieves near-optimal sample complexity.

AltSVM scales efficiently and outperforms baselines.

Method improves ranking accuracy on real datasets.

Abstract

In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between $d$ possible items; from these we need to predict preferences of the users for items they have not yet seen. We do so by fitting a rank $r$ score matrix to the pairwise data, and provide two main contributions: (a) we show that an algorithm based on convex optimization provides good generalization guarantees once each user provides as few as $O(r\log^2 d)$ pairwise comparisons -- essentially matching the sample complexity required in the related matrix completion setting (which uses actual numerical as opposed to pairwise information), and (b) we develop a large-scale non-convex implementation, which we call AltSVM, that trains a factored form of the matrix via alternating minimization (which we show reduces to alternating SVM problems), and scales and parallelizes very well to large problem settings. It also outperforms common baselines on many moderately large popular collaborative filtering datasets in both NDCG and in other measures of ranking performance.