Conformal Robust Set Estimation
Alejandro Cholaquidis, Emilien Joly, Leonardo Moreno
TLDR
This paper introduces a robust conformal prediction method using a half-mass radius non-conformity score for valid and robust set estimation.
Key contributions
- Proposes a robust conformal prediction method based on a half-mass radius non-conformity score.
- Ensures marginal validity for any sample size and convergence to a robust population central set.
- Establishes exponential concentration and tail bounds for empirical region deviation.
- Justifies using robust geometric scores for heavy-tailed or multi-modal distributions.
Why it matters
Standard conformal prediction struggles with outliers and heavy tails. This work provides a statistically sound, robust alternative using a novel geometric score. It significantly enhances the reliability of set estimation in challenging data environments.
Original 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.
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