Conformal Robust Set Estimation

TL;DR

This paper introduces a robust conformal prediction method using a geometric score based on nearest neighbors, ensuring valid coverage and convergence even with outliers or heavy tails.

Contribution

It proposes a new conformal region construction with robustness guarantees and convergence properties under mild regularity conditions.

Findings

Conformal regions are marginally valid for any sample size.

Regions converge in probability to a robust population central set.

Provides exponential concentration and tail bounds for deviation quantification.

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.