Conformal Prediction Intervals with Tail-Specific Guarantees
Simone Cuonzo, Nina Deliu
math.ST, q-fin.RM, stat.ME, stat.ML
Submitted: 2026-06-16
License: http://creativecommons.org/licenses/by/4.0/
The gist: This paper extends classical conformal frameworks for constructing prediction intervals with global marginal coverage 1-alpha to intervals that provide explicitly calibrated guarantees for the upper
Terminology
Abstract
This paper extends classical conformal frameworks for constructing prediction intervals with global marginal coverage 1-alpha to intervals that provide explicitly calibrated guarantees for the upper and lower tails separately. Focusing on split conformal prediction, we first construct lower and upper one-sided conformal intervals that achieve marginal validity, and then derive the induced two-sided interval by intersection. Theoretical results prove both tail-specific and global marginal coverage of the induced two-sided interval. Results are presented first for the exchangeable setting, where coverage has finite-sample guarantees, and then for non-exchangeable data, where guarantees are asymptotic. Simulation studies show that the proposed approach achieves improved directional calibration relative to classical two-sided intervals, especially relevant in skewed data. Finally, the benefit of the proposed framework is showcased in a financial application, where one aims for return maximization while seeking strict control on the left tail.
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