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.

翻译：共形预测（Conformal Prediction, CP）为不确定性量化提供了一个统计框架，能够构建具有覆盖保证的预测集。虽然CP产生的预测集大小不受控制，但后向共形预测（Backward Conformal Prediction, BCP）通过强制设定预测集大小的预定义上界并估计由此产生的覆盖保证，从而反转了这一范式。然而，BCP框架中马尔可夫不等式引入的松弛性导致估计的覆盖界与经验覆盖之间存在显著差距。本文提出ST-BCP这一新方法，通过引入数据依赖的非共形分数变换来缩小覆盖差距。具体而言，我们设计了一种可计算的变换，并证明其性能优于基线恒等变换。大量实验表明，我们的方法在常用基准测试中将平均覆盖差距从4.20%降低至1.12%。