Conformal Prediction Intervals with Tail-Specific Guarantees

2026-06-16

AI Summary

This work addresses a key limitation of traditional conformal prediction, which guarantees only marginal coverage without independent control over upper and lower tail risks. The authors propose a novel split-conformal approach that constructs one-sided prediction intervals—each marginally valid for its respective tail—and derives a two-sided interval via their intersection. This framework provides, for the first time, finite-sample or asymptotic guarantees of tail-specific coverage. By moving beyond the conventional focus on overall coverage, the method significantly improves directional calibration in simulations with skewed data and enables practical applications such as financial portfolio optimization, where it effectively supports return maximization while rigorously controlling left-tail risk.

Abstract

This paper extends classical conformal frameworks for constructing prediction intervals with global marginal coverage $1-α$ 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.

Problem

• Conformal Prediction
• Prediction Intervals
• Tail Coverage
• Marginal Validity
• Directional Calibration

Innovation

• Conformal Prediction
• Tail-Specific Coverage
• Split Conformal
• Directional Calibration
• Prediction Intervals