Conformal Robust Set Estimation

arXiv:2604.18441v2 Announce Type: replace-cross Abstract: We introduce a robust conformal prediction method based on the half-mass radius P(x):=inf{r>0:P(B(x,r))>1/2}. Its empirical version is exactly the distance from a point to its mathbf{k}-th nearest neighbour, with mathbf{k}=lfloor n/2rfloor+1. The resulting conformal sets retain finite-sample marginal validity and asymptotically target the robust population central set Qba:={xinR^d:P(x)leeta_alpha}. We prove consistency in symmetric-difference probability, derive non-asymptotic exponential bounds and obtain the rate O((log n/n)^{1/2}) under a local mass condition. Under the same local regularity on the uncontaminated law, we also establish quantitative O(eta) stability, uniformly over arbitrary contaminations of sufficiently small mass eta, prove Hausdorff convergence of the empirical central sets, and provide computable ball-based representations using only pairwise distances.

Source: arXiv cs.LG | 2026-09-29