# Learning Rich Rankings

arXiv: https://arxiv.org/abs/2312.15081 · HTML: https://mlsanity.com/paper/2312.15081/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Deep linear neural networks with arbitrary loss: All local minima are global](https://mlsanity.com/paper/1712.01473/) (2017)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Minimax-optimal Inference from Partial Rankings](https://mlsanity.com/paper/1406.5638/) (2014)
- [Learning Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/1603.07323/) (2016)
- [Discovering Context Effects from Raw Choice Data](https://mlsanity.com/paper/1902.03266/) (2019)
- [Exponential Family Embeddings](https://mlsanity.com/paper/1608.00778/) (2016)
- [Learning from Comparisons and Choices](https://mlsanity.com/paper/1704.07228/) (2017)
- [Pairwise Choice Markov Chains](https://mlsanity.com/paper/1603.02740/) (2016)
- [Learning Mixed Multinomial Logit Model from Ordinal Data](https://mlsanity.com/paper/1411.0073/) (2014)

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

- [Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting](https://mlsanity.com/paper/2402.18697/) (2024)
- [Leveraging Sparsity for Sample-Efficient Preference Learning: A Theoretical Perspective](https://mlsanity.com/paper/2501.18282/) (2025)
- [When the Universe is Too Big: Bounding Consideration Probabilities for Plackett-Luce Rankings](https://mlsanity.com/paper/2401.11016/) (2024)
- [Hypothesis Testing for Generalized Thurstone Models](https://mlsanity.com/paper/2512.02912/) (2025)
- [DeepHalo: A Neural Choice Model with Controllable Context Effects](https://mlsanity.com/paper/2601.04616/) (2026)
- [Generalized Top-k Mallows Model for Ranked Choices](https://mlsanity.com/paper/2510.22040/) (2025)
- [A Differentiable Bayesian Relaxation for Latent Partial-Order Inference](https://mlsanity.com/paper/2605.06976/) (2026)
- [MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment](https://mlsanity.com/paper/2608.25200/) (2026)

## Abstract (arXiv)

Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total ordering. Explicit mixture models have provided some tools for modelling multimodal ranking data, though learning such models from data is often difficult. In this work, we contribute a contextual repeated selection (CRS) model that leverages recent advances in choice modeling to bring a natural multimodality and richness to the rankings space. We provide rigorous theoretical guarantees for maximum likelihood estimation under the model through structure-dependent tail risk and expected risk bounds. As a by-product, we also furnish the first tight bounds on the expected risk of maximum likelihood estimators for the multinomial logit (MNL) choice model and the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on the PL ranking model. The CRS model significantly outperforms existing methods for modeling real world ranking data in a variety of settings, from racing to rank choice voting.