ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation

TL;DR

ST-BCP is a new method that improves backward conformal prediction by transforming non-conformity scores, significantly reducing the coverage gap and providing tighter coverage guarantees.

Contribution

The paper introduces a data-dependent transformation of non-conformity scores that narrows the coverage gap in backward conformal prediction, outperforming baseline methods.

Findings

Reduces average coverage gap from 4.20% to 1.12% on benchmarks.

Develops a computable transformation that outperforms the identity transformation.

Extensive experiments validate the effectiveness of the proposed method.

Abstract

Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees. While CP yields uncontrolled prediction set sizes, Backward Conformal Prediction (BCP) inverts this paradigm by enforcing a predefined upper bound on set size and estimating the resulting coverage guarantee. However, the looseness induced by Markov's inequality within the BCP framework causes a significant gap between the estimated coverage bound and the empirical coverage. In this work, we introduce ST-BCP, a novel method that introduces a data-dependent transformation of nonconformity scores to narrow the coverage gap. In particular, we develop a computable transformation and prove that it outperforms the baseline identity transformation. Extensive experiments demonstrate the effectiveness of our method, reducing the average coverage gap from 4.20\% to 1.12\% on common benchmarks.