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.

Although the population (i.e, infinite-particle) limit dynamics of SVGD is well characterized, its behavior in the finite-particle regime is far less understood.

Although the population (i.e, infinite-particle) limit dynamics of SVGD is well characterized, its behavior in the finite-particle regime is far less understood.

In such a setting, distribution-free risk bounds are impossible, and the best one could hope for is a fully empirical data-dependent bound.