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

2026-02-02

AI Summary

This work addresses the overly conservative coverage guarantees of Backward Conformal Prediction, which stem from its reliance on Markov’s inequality and result in a significant gap between theoretical bounds and empirical coverage. To mitigate this limitation, the authors propose a data-driven transformation of nonconformity scores that replaces the identity mapping within the Backward Conformal Prediction framework. They theoretically demonstrate that this approach yields substantially tighter coverage bounds by integrating conformal prediction theory with refined probabilistic inequalities. Empirical evaluations on standard benchmarks show that the proposed method reduces the average coverage gap from 4.20% to 1.12%, markedly improving both the practical utility and tightness of the resulting prediction intervals.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Data transparency and provenance

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.

Problem

• Conformal Prediction
• Backward Conformal Prediction
• Coverage Bound
• Non-Conformity Score
• Markov's Inequality

Innovation

• Conformal Prediction
• Backward Conformal Prediction
• Non-conformity Score Transformation
• Coverage Bound
• Uncertainty Quantification