# Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations

arXiv: https://arxiv.org/abs/2502.14105 · HTML: https://mlsanity.com/paper/2502.14105/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [The iWildCam 2020 Competition Dataset](https://mlsanity.com/paper/2004.10340/) (2020)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Certifying Confidence via Randomized Smoothing](https://mlsanity.com/paper/2009.08061/) (2020)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Provably Robust Conformal Prediction with Improved Efficiency](https://mlsanity.com/paper/2404.19651/) (2024)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [Valid model-free spatial prediction](https://mlsanity.com/paper/2006.15640/) (2020)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)

## Built on by (most cited first, 12 of 12)

- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)
- [Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation](https://mlsanity.com/paper/2601.22298/) (2026)
- [When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Prediction](https://mlsanity.com/paper/2602.12616/) (2026)
- [Conformal Prediction via Transported Beta Laws](https://mlsanity.com/paper/2605.19024/) (2026)
- [Coverage Guarantees for Pseudo-Calibrated Conformal Prediction under Distribution Shift](https://mlsanity.com/paper/2602.14913/) (2026)
- [When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination](https://mlsanity.com/paper/2605.06204/) (2026)
- [Conformalized Large Language Models under Configuration Shift](https://mlsanity.com/paper/2608.01460/) (2026)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)
- [Multi-source conformal prediction: leveraging heterogeneity via localization](https://mlsanity.com/paper/2609.14531/) (2026)
- [Conformal Bayes under Continuous Label Shift: Sensitivity Analysis and the Limits of Exact Validity](https://mlsanity.com/paper/2609.27976/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)

## Abstract (arXiv)

Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable one-dimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.