# Probabilistically robust conformal prediction

arXiv: https://arxiv.org/abs/2307.16360 · HTML: https://mlsanity.com/paper/2307.16360/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Human-Centered Tools for Coping with Imperfect Algorithms during Medical Decision-Making](https://mlsanity.com/paper/1902.02960/) (2019)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [NATTACK: Learning the Distributions of Adversarial Examples for an Improved Black-Box Attack on Deep Neural Networks](https://mlsanity.com/paper/1905.00441/) (2019)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Cautious Deep Learning](https://mlsanity.com/paper/1805.09460/) (2018)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Improving Uncertainty Quantification of Deep Classifiers via Neighborhood Conformal Prediction: Novel Algorithm and Theoretical Analysis](https://mlsanity.com/paper/2303.10694/) (2023)

## Built on by (most cited first, 25 of 25)

- [Provably Robust Conformal Prediction with Improved Efficiency](https://mlsanity.com/paper/2404.19651/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibration](https://mlsanity.com/paper/2406.06818/) (2024)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Robust Yet Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2407.09165/) (2024)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Verifiably Robust Conformal Prediction](https://mlsanity.com/paper/2405.18942/) (2024)
- [Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imaging](https://mlsanity.com/paper/2411.04376/) (2024)
- [COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuits](https://mlsanity.com/paper/2403.11348/) (2024)
- [The Pitfalls and Promise of Conformal Inference Under Adversarial Attacks](https://mlsanity.com/paper/2405.08886/) (2024)
- [Direct Prediction Set Minimization via Bilevel Conformal Classifier Training](https://mlsanity.com/paper/2506.06599/) (2025)
- [Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guide](https://mlsanity.com/paper/2502.14833/) (2025)
- [Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability](https://mlsanity.com/paper/2506.07804/) (2025)
- [Trustworthy AI Must Account for Interactions](https://mlsanity.com/paper/2504.07170/) (2025)
- [Provably Reliable Conformal Prediction Sets in the Presence of Data Poisoning](https://mlsanity.com/paper/2410.09878/) (2024)
- [Robust Conformal Prediction with a Single Binary Certificate](https://mlsanity.com/paper/2503.05239/) (2025)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)
- [One Sample is Enough to Make Conformal Prediction Robust](https://mlsanity.com/paper/2506.16553/) (2025)
- [Multi-Distribution Robust Conformal Prediction](https://mlsanity.com/paper/2601.02998/) (2026)
- [Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Model](https://mlsanity.com/paper/2403.15025/) (2024)
- [The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets](https://mlsanity.com/paper/2511.05523/) (2025)
- [Ensuring Calibration Robustness in Split Conformal Prediction Under Adversarial Attacks](https://mlsanity.com/paper/2511.18562/) (2025)
- [Conformal Margin Risk Minimization: An Envelope Framework for Robust Learning under Label Noise](https://mlsanity.com/paper/2604.06468/) (2026)
- [Conformity Breaks Conformal Prediction](https://mlsanity.com/paper/2609.04445/) (2026)
- [Robust Conformal Intrusion Detection via Traffic-Aware Calibration and Attack-Orbit Invariance](https://mlsanity.com/paper/2609.19241/) (2026)

## Abstract (arXiv)

Conformal prediction (CP) is a framework to quantify uncertainty of machine learning classifiers including deep neural networks. Given a testing example and a trained classifier, CP produces a prediction set of candidate labels with a user-specified coverage (i.e., true class label is contained with high probability). Almost all the existing work on CP assumes clean testing data and there is not much known about the robustness of CP algorithms w.r.t natural/adversarial perturbations to testing examples. This paper studies the problem of probabilistically robust conformal prediction (PRCP) which ensures robustness to most perturbations around clean input examples. PRCP generalizes the standard CP (cannot handle perturbations) and adversarially robust CP (ensures robustness w.r.t worst-case perturbations) to achieve better trade-offs between nominal performance and robustness. We propose a novel adaptive PRCP (aPRCP) algorithm to achieve probabilistically robust coverage. The key idea behind aPRCP is to determine two parallel thresholds, one for data samples and another one for the perturbations on data (aka "quantile-of-quantile" design). We provide theoretical analysis to show that aPRCP algorithm achieves robust coverage. Our experiments on CIFAR-10, CIFAR-100, and ImageNet datasets using deep neural networks demonstrate that aPRCP achieves better trade-offs than state-of-the-art CP and adversarially robust CP algorithms.