Apr 20, 2026 · math.STJ/K move · Enter open · S save
Alejandro Cholaquidis, Emilien Joly, Leonardo Moreno
*Centro de Matem´atica, Facultad de Ciencias, Universidad de la Rep´ublica, Uruguay · †Centro de Investigaci´on en Matem´aticas (CIMAT), M´exico · ‡Departamento de M´etodos Cuantitativos, Facultad de Ciencias Econ´omicas y de Administraci´on, Universidad de la Rep´ublica, Uruguay
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
(⌊n/2⌋+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.