ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917504188678144 |
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| author | Liu, Junxian Zeng, Hao Wei, Hongxin |
| author_facet | Liu, Junxian Zeng, Hao Wei, Hongxin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_01733 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation Liu, Junxian Zeng, Hao Wei, Hongxin Machine Learning 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. |
| title | ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.01733 |