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

• URL: http://arxiv.org/abs/2602.01733v1
• Date: Mon, 02 Feb 2026 07:18:35 GMT
• Title: ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation
• Authors: Junxian Liu, Hao Zeng, Hongxin Wei,
• Abstract summary: Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees.<n>BCP inverts this paradigm by enforcing a predefined upper bound on set size and estimating the resulting coverage guarantee.<n>We introduce ST-BCP, a novel method that introduces a data-dependent transformation of nonconformity scores to narrow the coverage gap.
• Score: 18.272247805086284
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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