mlsanityData to 7 Oct 2026

Conformal Robust Set Estimation

arXiv 2604.18441 ↗First posted 20 Apr 2026math.ST cs.LG stat.MLcited by 0

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Abstract (arXiv)

We introduce a robust conformal prediction method based on the half-mass radius dP(x):=infr>0:P(B(x,r))>1/2. Its empirical version is exactly the distance from a point to its k-th nearest neighbour, with k=lfloor n/2rfloor+1. The resulting conformal sets retain finite-sample marginal validity and asymptotically target the robust population central set Qba:=x∈Rd:dP(x)≤βα. We prove consistency in symmetric-difference probability, derive non-asymptotic exponential bounds and obtain the rate O((log n/n)1/2) under a local mass condition. Under the same local regularity on the uncontaminated law, we also establish quantitative O(η) stability, uniformly over arbitrary contaminations of sufficiently small mass η, prove Hausdorff convergence of the empirical central sets, and provide computable ball-based representations using only pairwise distances.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 15 of its 24 references that are in the map. First posted on arXiv 20 Apr 2026.

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References · 15

  1. 2019Conformalized Quantile Regressioncited by 620
  2. 2022Conformal prediction beyond exchangeabilitycited by 348
  3. 2021Testing for Outliers with Conformal p-valuescited by 133
  4. 2022Conformal Inference for Online Prediction with Arbitrary Distribution Shiftscited by 123
  5. 2020Conformal Prediction: a Unified Review of Theory and New Challengescited by 118
  6. 2013A Conformal Prediction Approach to Explore Functional Datacited by 85
  7. 2020Robust Validation: Confident Predictions Even When Distributions Shiftcited by 82
  8. 2019Prediction and outlier detection in classification problemscited by 44
  9. 2021Conformal Bayesian Computationcited by 38
  10. 2021Conformal Prediction Bands for Multivariate Functional Datacited by 28
  11. 2014Robust Topological Inference: Distance To a Measure and Kernel Distancecited by 25
  12. 2022Label Noise Robustness of Conformal Predictioncited by 19
3 more
  1. 2024Split Conformal Prediction under Data Contaminationcited by 12
  2. 2025Robust Conformal Outlier Detection under Contaminated Reference Datacited by 12
  3. 2024GROS: A General Robust Aggregation Strategycited by 1

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