[论文] Conformal Prediction Sets Quantify Information Gain: A Theoretical Per...

论文概要

研究领域: ML
作者: Kevin Zhang, Stephen Bates
发布时间: 2026-10-06
arXiv: 2610.08785

中文摘要

保形预测（conformal prediction）是一种流行的不确定性量化工具，输出具有有限样本覆盖保证的预测集。虽然预测集大小常用作不确定性的启发式度量，但其信息论基础仍然理解不足。本工作使用针对集合值预测的决策论熵泛化为这种解释提供了基础。具体而言，我们引入了一族基于保形预测集大小和覆盖率的广义信息度量。值得注意的是，香农互信息允许用这些度量的精确积分表示。我们表明在标准分类设置中，来自额外信息的保形集大小的减少（i）被该族的依赖于校准的成员所夹逼，（ii）服从数据处理不等式，两者都相差有限样本校准和模型误差项。总之，我们的结果将保形预测与经典信息论量正式联系起来，并证明了将集合大小减少用作信息增益指标的合理性。我们在11个分类设置上验证了这一理论，并表明在贪心特征选择中，集合大小减少和香农互信息可以对特征进行不同的排序。

原文摘要

Conformal prediction is a popular tool for uncertainty quantification that outputs prediction sets with finite-sample coverage guarantees. While prediction set size is commonly used as a heuristic measure of uncertainty, the information-theoretic basis for this interpretation remains poorly understood. In this work, we provide such a foundation using a decision-theoretic generalization of entropy tailored to set-valued prediction. In particular, we introduce a family of generalized information measures based on the size and coverage of conformal prediction sets. Notably, Shannon mutual information admits an exact integral representation in terms of these measures. We then show that, in standard classification settings, the reduction in conformal set size from additional information (i) is ...

自动采集于 2026-10-08

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