# Learning-to-Rank with Partitioned Preference: Fast Estimation for the Plackett-Luce Model

arXiv: https://arxiv.org/abs/2006.05067 · HTML: https://mlsanity.com/paper/2006.05067/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Alignment of Diffusion Models: Fundamentals, Challenges, and Future](https://mlsanity.com/paper/2409.07253/) (2024)
- [Language Modelling via Learning to Rank](https://mlsanity.com/paper/2110.06961/) (2021)
- [Gradient-Boosted Decision Tree for Listwise Context Model in Multimodal Review Helpfulness Prediction](https://mlsanity.com/paper/2305.12678/) (2023)
- [Fast Slate Policy Optimization: Going Beyond Plackett-Luce](https://mlsanity.com/paper/2308.01566/) (2023)
- [Fast Learning of MNL Model from General Partial Rankings with Application to Network Formation Modeling](https://mlsanity.com/paper/2112.15575/) (2021)
- [Quotient DAGs for Off-Policy Evaluation:Forward-Flow Importance Sampling and Exact Slate Propensities](https://mlsanity.com/paper/2605.29500/) (2026)
- [Credit-assigned Policy Gradient for Early Stage Retrieval in Two-stage Ranking](https://mlsanity.com/paper/2605.26385/) (2026)
- [Scoring Is Not Enough: Addressing Gaps in Utility-fairness Trade-offs for Ranking](https://mlsanity.com/paper/2606.26369/) (2026)
- [Measure Less, Know More: Self-Supervised Test-Time Feature Acquisition](https://mlsanity.com/paper/2610.03454/) (2026)

## Abstract (arXiv)

We investigate the Plackett-Luce (PL) model based listwise learning-to-rank (LTR) on data with partitioned preference, where a set of items are sliced into ordered and disjoint partitions, but the ranking of items within a partition is unknown. Given N items with M partitions, calculating the likelihood of data with partitioned preference under the PL model has a time complexity of O(N+S!), where S is the maximum size of the top M-1 partitions. This computational challenge restrains most existing PL-based listwise LTR methods to a special case of partitioned preference, top-K ranking, where the exact order of the top K items is known. In this paper, we exploit a random utility model formulation of the PL model, and propose an efficient numerical integration approach for calculating the likelihood and its gradients with a time complexity O(N+S3). We demonstrate that the proposed method outperforms well-known LTR baselines and remains scalable through both simulation experiments and applications to real-world eXtreme Multi-Label classification tasks.