改进逆向共形预测，缩小预测置信集覆盖率差距。
Improving Backward Conformal Prediction via Non-Conformity Score Transformation
- 通过数据相关变换非符合度分数，优化逆向共形预测
- 在基准测试上将覆盖率差距从4.20%降至1.12%
- 适合关注不确定性量化与置信集控制的研究者
共形预测（CP）提供了一种不确定性量化统计框架，可构建具有覆盖率保证的预测集。尽管如此，标准CP会导致预测集大小不可控。逆向共形预测（BCP）反转这一范式，强制设定预测集大小上限，并估计对应的覆盖率保证。然而，BCP框架中使用马尔可夫不等式引入的松散性，导致估计覆盖率与实际覆盖率之间存在显著差距。本文提出ST-BCP，一种新型方法，通过引入数据依赖的非符合度分数变换来缩小覆盖率差距。我们设计了一种可计算的变换，并证明其优于基础的恒等变换。大量实验表明，该方法可将常见基准上的平均覆盖率差距从4.20%降低至1.12%。
原文摘要 · Abstract (English)
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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