mlsanityData to 7 Oct 2026

Probabilistically robust conformal prediction

arXiv 2307.16360 ↗First posted 31 Jul 2023cs.LG stat.MLcited by 25

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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.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 24 of its 37 references that are in the map. First posted on arXiv 31 Jul 2023.

Builds on

24 of 37 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  3. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  4. 2019Conformalized Quantile Regressioncited by 620
  5. 2019Conformal Prediction Under Covariate Shiftcited by 511
  6. 2020Classification with Valid and Adaptive Coveragecited by 390
  7. 2020Uncertainty Sets for Image Classifiers using Conformal Predictioncited by 365
  8. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  9. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
  10. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 270
  11. 2019Predictive inference with the jackknife+cited by 206
  12. 2019Human-Centered Tools for Coping with Imperfect Algorithms during Medical Decision-Makingcited by 109
12 more
  1. 2020A survey on domain adaptation theory: learning bounds and theoretical guaranteescited by 109
  2. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 99
  3. 2019NATTACK: Learning the Distributions of Adversarial Examples for an Improved Black-Box Attack on Deep Neural Networkscited by 94
  4. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  5. 2020Robust Validation: Confident Predictions Even When Distributions Shiftcited by 82
  6. 2019Flexible distribution-free conditional predictive bands using density estimatorscited by 64
  7. 2019Adaptive, Distribution-Free Prediction Intervals for Deep Networkscited by 56
  8. 2019Prediction and outlier detection in classification problemscited by 44
  9. 2022Probabilistically Robust Learning: Balancing Average- and Worst-case Performancecited by 36
  10. 2018Cautious Deep Learningcited by 35
  11. 2019Conformal prediction with localizationcited by 22
  12. 2023Improving Uncertainty Quantification of Deep Classifiers via Neighborhood Conformal Prediction: Novel Algorithm and Theoretical Analysiscited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 11; 2025: 10; 2026: 4.

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  1. 2024Provably Robust Conformal Prediction with Improved Efficiencycited by 27
  2. 2024Conformal Prediction: A Data Perspectivecited by 25
  3. 2024Conformal Prediction for Causal Effects of Continuous Treatmentscited by 19
  4. 2024Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibrationcited by 18
  5. 2024Robust Yet Efficient Conformal Prediction Setscited by 16
  6. 2025Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbationscited by 11
  7. 2024Verifiably Robust Conformal Predictioncited by 10
  8. 2024Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imagingcited by 10
  9. 2024COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuitscited by 9
  10. 2024The Pitfalls and Promise of Conformal Inference Under Adversarial Attackscited by 8
  11. 2025Direct Prediction Set Minimization via Bilevel Conformal Classifier Trainingcited by 8
  12. 2025Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guidecited by 6
13 more
  1. 2025Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliabilitycited by 6
  2. 2024Provably Reliable Conformal Prediction Sets in the Presence of Data Poisoningcited by 4
  3. 2025Robust Conformal Prediction with a Single Binary Certificatecited by 4
  4. 2025Trustworthy AI Must Account for Interactionscited by 4
  5. 2025Efficient Robust Conformal Prediction via Lipschitz-Bounded Networkscited by 4
  6. 2025One Sample is Enough to Make Conformal Prediction Robustcited by 4
  7. 2024Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Modelcited by 1
  8. 2026Multi-Distribution Robust Conformal Predictioncited by 1
  9. 2025The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Marketscited by 0
  10. 2025Ensuring Calibration Robustness in Split Conformal Prediction Under Adversarial Attackscited by 0
  11. 2026Conformal Margin Risk Minimization: An Envelope Framework for Robust Learning under Label Noisecited by 0
  12. 2026Conformity Breaks Conformal Predictioncited by 0
  13. 2026Robust Conformal Intrusion Detection via Traffic-Aware Calibration and Attack-Orbit Invariancecited by 0