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This research introduces ST-BCP, a method that applies data-dependent transformations to nonconformity scores within Backward Conformal Prediction frameworks. By addressing the looseness caused by Markov's inequality, the technique significantly narrows the gap between estimated and empirical coverage guarantees on standard benchmarks. The work advances uncertainty quantification in machine learning models without relying on external AI or quantum hardware capabilities.
Improving Backward Conformal Prediction via Non-Conformity Score Transformation
arXiv:2602.01733v3 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2602.01733 [stat.ML]
(or arXiv:2602.01733v3 [stat.ML] for this version)
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