# Covariate Assisted Entity Ranking with Sparse Intrinsic Scores

arXiv: https://arxiv.org/abs/2407.08814 · HTML: https://mlsanity.com/paper/2407.08814/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Uncertainty Quantification of MLE for Entity Ranking with Covariates](https://mlsanity.com/paper/2212.09961/) (2022)
- [Spectral Ranking Inferences based on General Multiway Comparisons](https://mlsanity.com/paper/2308.02918/) (2023)
- [A unified analysis of likelihood-based estimators in the Plackett--Luce model](https://mlsanity.com/paper/2306.02821/) (2023)
- [Learning Mixtures of Random Utility Models with Features from Incomplete Preferences](https://mlsanity.com/paper/2006.03869/) (2020)

## Built on by (most cited first, 7 of 7)

- [Dual Active Learning for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2410.02504/) (2024)
- [Robust Reinforcement Learning from Human Feedback for Large Language Models Fine-Tuning](https://mlsanity.com/paper/2504.03784/) (2025)
- [Low-Rank Contextual Reinforcement Learning from Heterogeneous Human Feedback](https://mlsanity.com/paper/2412.19436/) (2024)
- [Uncertainty Quantification for Large Language Model Reward Learning under Heterogeneous Human Feedback](https://mlsanity.com/paper/2512.03208/) (2025)
- [A Judge-Aware Ranking Framework for Evaluating Large Language Models without Ground Truth](https://mlsanity.com/paper/2601.21817/) (2026)
- [Reinforcement Learning from Human Feedback: A Statistical Perspective](https://mlsanity.com/paper/2604.02507/) (2026)
- [Maximum Likelihood Estimation for Entity Ranking under Iterative Synthetic Data Augmentation](https://mlsanity.com/paper/2609.32987/) (2026)

## Abstract (arXiv)

This paper addresses the item ranking problem with associate covariates, focusing on scenarios where the preference scores can not be fully explained by covariates, and the remaining intrinsic scores, are sparse. Specifically, we extend the pioneering Bradley-Terry-Luce (BTL) model by incorporating covariate information and considering sparse individual intrinsic scores. Our work introduces novel model identification conditions and examines the regularized penalized Maximum Likelihood Estimator (MLE) statistical rates. We then construct a debiased estimator for the penalized MLE and analyze its distributional properties. Additionally, we apply our method to the goodness-of-fit test for models with no latent intrinsic scores, namely, the covariates fully explaining the preference scores of individual items. We also offer confidence intervals for ranks. Our numerical studies lend further support to our theoretical findings, demonstrating validation for our proposed method