Conformal Robust Set Estimation

• URL: http://arxiv.org/abs/2604.18441v1
• Date: Mon, 20 Apr 2026 15:59:23 GMT
• Title: Conformal Robust Set Estimation
• Abstract summary: We propose a robust conformal method based on a non-conformity score defined as the half-mass radius around a point.<n>We show that the resulting conformal regions are marginally valid for any sample size and converge in probability to a robust population central set.
• Score: 41.99844472131922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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