# Max-Rank: Efficient Multiple Testing for Conformal Prediction

arXiv: https://arxiv.org/abs/2311.10900 · HTML: https://mlsanity.com/paper/2311.10900/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 78 references that are in the map.
- First posted on arXiv 17 Nov 2023.

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

- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Consistent Accelerated Inference via Confident Adaptive Transformers](https://mlsanity.com/paper/2104.08803/) (2021)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Conformal Prediction Sets with Limited False Positives](https://mlsanity.com/paper/2202.07650/) (2022)
- [Multi-Agent Reachability Calibration with Conformal Prediction](https://mlsanity.com/paper/2304.00432/) (2023)
- [Confident Object Detection via Conformal Prediction and Conformal Risk Control: an Application to Railway Signaling](https://mlsanity.com/paper/2304.06052/) (2023)
- [Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures](https://mlsanity.com/paper/1808.09011/) (2018)
- [Multiple testing under negative dependence](https://mlsanity.com/paper/2212.09706/) (2022)
- [Familywise Error Rate Control via Knockoffs](https://mlsanity.com/paper/1505.06549/) (2015)

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

- [Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction](https://mlsanity.com/paper/2403.07263/) (2024)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Conformal forecasting for surgical instrument trajectory](https://mlsanity.com/paper/2503.04191/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Probabilistic Object Detection with Conformal Prediction](https://mlsanity.com/paper/2605.07549/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)
- [Dream2Discern: Learning from Hard Latent Variants for Runtime Failure Prediction in Multi-Agent Systems](https://mlsanity.com/paper/2610.16071/) (2026)

## Abstract (arXiv)

Multiple hypothesis testing (MHT) frequently arises in scientific inquiries, and concurrent testing of multiple hypotheses inflates the risk of Type-I errors or false positives, rendering MHT corrections essential. This paper addresses MHT in the context of conformal prediction, a flexible framework for predictive uncertainty quantification. Some conformal applications give rise to simultaneous testing, and positive dependencies among tests typically exist. We introduce textttmax-rank, a novel correction that exploits these dependencies whilst efficiently controlling the family-wise error rate. Inspired by existing permutation-based corrections, textttmax-rank leverages rank order information to improve performance and integrates readily with any conformal procedure. We establish its theoretical and empirical advantages over the common Bonferroni correction and its compatibility with conformal prediction, highlighting the potential to strengthen predictive uncertainty estimates.