SQL-Rank: A Listwise Approach to Collaborative Ranking

TL;DR

This paper introduces SQL-Rank, a novel listwise collaborative ranking algorithm that models permutations with a low rank score matrix, outperforming existing methods in recommendation systems.

Contribution

The paper presents SQL-Rank, a linear-time, tie- and missing data-compatible listwise ranking algorithm with a theoretical framework and asymptotic analysis for collaborative ranking.

Findings

SQL-Rank outperforms Weighted-MF and BPR in implicit feedback scenarios.

SQL-Rank achieves competitive results compared to explicit feedback algorithms.

Theoretical analysis provides asymptotic statistical rates for the method.

Abstract

In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on treating either each rating or each pairwise comparison as an independent instance respectively. By extending the work of (Cao et al. 2007), we cast listwise collaborative ranking as maximum likelihood under a permutation model which applies probability mass to permutations based on a low rank latent score matrix. We present a novel algorithm called SQL-Rank, which can accommodate ties and missing data and can run in linear time. We develop a theoretical framework for analyzing listwise ranking methods based on a novel representation theory for the permutation model. Applying this framework to collaborative ranking, we derive asymptotic statistical rates as the number of users and items grow together. We conclude by demonstrating that our SQL-Rank method often outperforms current state-of-the-art algorithms for implicit feedback such as Weighted-MF and BPR and achieve favorable results when compared to explicit feedback algorithms such as matrix factorization and collaborative ranking.