# Distribution-informed Efficient Conformal Prediction for Full Ranking

arXiv: https://arxiv.org/abs/2601.23128 · HTML: https://mlsanity.com/paper/2601.23128/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Large Language Models are Zero-Shot Rankers for Recommender Systems](https://mlsanity.com/paper/2305.08845/) (2023)
- [Simple, Robust and Optimal Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1512.08949/) (2015)
- [API Is Enough: Conformal Prediction for Large Language Models Without Logit-Access](https://mlsanity.com/paper/2403.01216/) (2024)
- [When Search Engine Services meet Large Language Models: Visions and Challenges](https://mlsanity.com/paper/2407.00128/) (2024)
- [Efficient computation of rankings from pairwise comparisons](https://mlsanity.com/paper/2207.00076/) (2022)
- [TRAQ: Trustworthy Retrieval Augmented Question Answering via Conformal Prediction](https://mlsanity.com/paper/2307.04642/) (2023)
- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Optimal Full Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2101.08421/) (2021)
- [Recommendation Systems with Distribution-Free Reliability Guarantees](https://mlsanity.com/paper/2207.01609/) (2022)
- [Response Quality Assessment for Retrieval-Augmented Generation via Conditional Conformal Factuality](https://mlsanity.com/paper/2506.20978/) (2025)
- [Aggregating Incomplete and Noisy Rankings](https://mlsanity.com/paper/2011.00810/) (2020)
- [Learning Concept Embeddings with Combined Human-Machine Expertise](https://mlsanity.com/paper/1509.07479/) (2015)
- [Uncertainty in Ranking](https://mlsanity.com/paper/2107.03459/) (2021)
- [Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method](https://mlsanity.com/paper/2109.13743/) (2021)
- [Structured Conformal Inference for Matrix Completion with Applications to Group Recommender Systems](https://mlsanity.com/paper/2404.17561/) (2024)
- [Transductive Conformal Inference for Full Ranking](https://mlsanity.com/paper/2501.11384/) (2025)

## Abstract (arXiv)

Quantifying uncertainty is critical for the safe deployment of ranking models in real-world applications. Recent work offers a rigorous solution using conformal prediction in a full ranking scenario, which aims to construct prediction sets for the absolute ranks of test items based on the relative ranks of calibration items. However, relying on upper bounds of non-conformity scores renders the method overly conservative, resulting in substantially large prediction sets. To address this, we propose Distribution-informed Conformal Ranking (DCR), which produces efficient prediction sets by deriving the exact distribution of non-conformity scores. In particular, we find that the absolute ranks of calibration items follow Negative Hypergeometric distributions, conditional on their relative ranks. DCR thus uses the rank distribution to derive non-conformity score distribution and determine conformal thresholds. We provide theoretical guarantees that DCR achieves improved efficiency over the baseline while ensuring valid coverage under mild assumptions. Extensive experiments demonstrate the superiority of DCR, reducing average prediction set size by up to 36%, while maintaining valid coverage.