# Conditional Testing based on Localized Conformal p-values

arXiv: https://arxiv.org/abs/2409.16829 · HTML: https://mlsanity.com/paper/2409.16829/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [A Burden Shared is a Burden Halved: A Fairness-Adjusted Approach to Classification](https://mlsanity.com/paper/2110.05720/) (2021)
- [De-Biased Two-Sample U-Statistics With Application To Conditional Distribution Testing](https://mlsanity.com/paper/2402.00164/) (2024)
- [MCODE: Multivariate Conditional Outlier Detection](https://mlsanity.com/paper/1505.04097/) (2015)

## Built on by (most cited first, 4 of 4)

- [Theoretical guarantees for change localization using conformal p-values](https://mlsanity.com/paper/2510.08749/) (2025)
- [Model-agnostic Selective Labeling with Provable Statistical Guarantees](https://mlsanity.com/paper/2510.14581/) (2025)
- [Reliable Inference in Edge-Cloud Model Cascades via Conformal Alignment](https://mlsanity.com/paper/2510.17543/) (2025)
- [Distribution-free root cause analysis](https://mlsanity.com/paper/2605.21627/) (2026)

## Abstract (arXiv)

In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.