# SQL-Rank: A Listwise Approach to Collaborative Ranking

arXiv: https://arxiv.org/abs/1803.00114 · HTML: https://mlsanity.com/paper/1803.00114/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2018.

## Built on by (most cited first, 8 of 8)

- [Ensuring User-side Fairness in Dynamic Recommender Systems](https://mlsanity.com/paper/2308.15651/) (2023)
- [LPOI: Listwise Preference Optimization for Vision Language Models](https://mlsanity.com/paper/2505.21061/) (2025)
- [Set2setRank: Collaborative Set to Set Ranking for Implicit Feedback based Recommendation](https://mlsanity.com/paper/2105.07377/) (2021)
- [Disentangled Representation for Diversified Recommendations](https://mlsanity.com/paper/2301.05492/) (2023)
- [Preference or Intent? Double Disentangled Collaborative Filtering](https://mlsanity.com/paper/2305.11084/) (2023)
- [Improving Lung Cancer Diagnosis and Survival Prediction with Deep Learning and CT Imaging](https://mlsanity.com/paper/2408.09367/) (2024)
- [A hierarchy tree data structure for behavior-based user segment representation](https://mlsanity.com/paper/2508.01115/) (2025)
- [Population-Level Generative Modeling for Ranking Data](https://mlsanity.com/paper/2608.08422/) (2026)

## Abstract (arXiv)

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.