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

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.

💡 Research Summary

Conformal prediction (CP) has become a cornerstone of distribution‑free uncertainty quantification, typically evaluated by two metrics: marginal coverage (the proportion of true responses that fall inside the predicted set) and average interval length (the size of the prediction set). The prevailing research agenda assumes that a method that improves both metrics is automatically superior. This paper challenges that assumption by introducing a simple yet powerful “Prejudicial Trick” (PT) that can artificially reduce average interval length while preserving the nominal marginal coverage, thereby exposing a fundamental weakness in the coverage‑length evaluation paradigm.

The Prejudicial Trick (PT).
Given a base CP algorithm A₁₋α(·; μ̂) and a test point x′, PT proceeds as follows: draw a uniform random variable U∈