Conformal Robust Set Estimation
For practitioners needing reliable prediction sets under heavy-tailed or outlier-prone data, this method offers a theoretically grounded robust alternative to standard conformal prediction.
The paper proposes a robust conformal prediction method using a non-conformity score based on the half-mass radius (distance to the (⌊n/2⌋+1)-nearest neighbor), achieving finite-sample marginal validity and convergence to a robust population central set with exponential concentration bounds, even under heavy-tailed or multi-modal distributions.
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.