Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better

TL;DR

This paper critically examines the standard metrics used in conformal prediction, revealing that shorter intervals can be artificially achieved without true improvement, and introduces a new metric to detect such misleading practices.

Contribution

It exposes the limitations of current coverage and length metrics in conformal prediction and proposes a new stability metric to identify deceptive interval improvements.

Findings

Prejudicial Trick can reduce interval length without losing coverage

PT introduces practical vulnerabilities with inconsistent intervals

Interval stability metric detects PT-like deceptive improvements

Abstract

Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick (PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provides extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques.