aiqbench analysis
This research advances the theoretical robustness of split conformal prediction by quantifying how training and calibration contamination affects interval length under Huber models. By establishing matching finite-sample upper and minimax lower bounds, the work provides rigorous guarantees for uncertainty quantification in non-ideal data environments. The findings are particularly relevant for practitioners deploying conformal methods where data integrity cannot be assumed.
Split Conformal Interval Length under Huber Contamination
arXiv:2610.15458v1 Announce Type: new Abstract: Existing analyses of interval length in split conformal prediction largely focus on clean data. However, how contamination at the training and calibration stages alters interval length relative to the corresponding clean population oracle remains understudied. In this paper, we consider Huber contamination and derive a finite-sample upper bound that holds uniformly over contaminating distributions, with leading terms scaling as $L(\delta_1+n_1^{-1/2}) +(n_2^{-1/2}+\delta_2)/((1-\delta_2)r_0)$, in addition to a clean-sample estimation term. We further establish a minimax lower bound matching the upper-bound rate up to constant factors on a regular asymmetric location submodel. For calibration contamination, we obtain an exact worst-case characterization of the population interval-length deviation. We also extend the upper-bound results to conformalized quantile regression and adaptive residual scores. Experiments on synthetic and real-world datasets provide empirical support for our theoretical findings on training and calibration contamination.
Abstract:Existing analyses of interval length in split conformal prediction largely focus on clean data. However, how contamination at the training and calibration stages alters interval length relative to the corresponding clean population oracle remains understudied. In this paper, we consider Huber contamination and derive a finite-sample upper bound that holds uniformly over contaminating distributions, with leading terms scaling as $L(\delta_1+n_1^{-1/2}) +(n_2^{-1/2}+\delta_2)/((1-\delta_2)r_0)$, in addition to a clean-sample estimation term. We further establish a minimax lower bound matching the upper-bound rate up to constant factors on a regular asymmetric location submodel. For calibration contamination, we obtain an exact worst-case characterization of the population interval-length deviation. We also extend the upper-bound results to conformalized quantile regression and adaptive residual scores. Experiments on synthetic and real-world datasets provide empirical support for our theoretical findings on training and calibration contamination.
Machine Learning (cs.LG)
arXiv:2610.15458 [cs.LG]
(or arXiv:2610.15458v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.15458 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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experiment_code/reference/original/runs/synthetic/synthetic/rep00/variance_inflate_0_scores.npy
experiment_code/reference/original/runs/synthetic/synthetic/rep00/variance_inflate_1_scores.npy
experiment_code/reference/original/runs/synthetic/synthetic/rep00/variance_inflate_2_scores.npy
experiment_code/reference/original/runs/synthetic/synthetic/rep00/variance_inflate_3_scores.npy
experiment_code/reference/original/runs/synthetic/synthetic/rep00/variance_inflate_mask_u.npy
experiment_code/requirements.txt
experiment_code/tests/test_core.py
experiment_code/tests/validate_runs.py
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