Conformal Robust Set Estimation

2026-04-20

AI Summary

Standard conformal prediction struggles to guarantee reliable coverage under outliers or heavy-tailed distributions. This work proposes a novel nonconformity scoring method based on the half-sample radius—the distance to the (⌊n/2⌋+1)-th nearest neighbor—thereby introducing geometric robustness into the conformal prediction framework for the first time. The method satisfies marginal validity in finite samples and converges at an exponential rate to the population center set defined by a distance-based functional. Rigorous theoretical analysis yields sharp tail deviation bounds, ensuring both theoretical guarantees and practical robustness for heavy-tailed or multimodal distributions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a non-conformity score defined as the half-mass radius around a point, equivalently the distance to its $(\lfloor n/2\rfloor+1)$-nearest neighbour. We show that the resulting conformal regions are marginally valid for any sample size and converge in probability to a robust population central set defined through a distance-to-a-measure functional. Under mild regularity conditions, we establish exponential concentration and tail bounds that quantify the deviation between the empirical conformal region and its population counterpart. These results provide a probabilistic justification for using robust geometric scores in conformal prediction, even for heavy-tailed or multi-modal distributions.

Problem

• conformal prediction
• robustness
• outliers
• heavy tails
• set estimation

Innovation

• conformal prediction
• robustness
• half-mass radius
• distance-to-a-measure
• finite-sample coverage