公平性与覆盖率的权衡：统一阈值会隐藏群体差异
On the Burden of Achieving Fairness in Conformal Prediction
- 用分布理论揭示统一阈值导致群体覆盖率偏差的不可消除性
- 发现等覆盖率与等集合大小两种公平定义本质冲突
- 实验证明群体分开或合并校准存在双向代价交换
分拆校准下的共形预测通常使用单一全局阈值，但可能掩盖评分分布的群体异质性，导致群体覆盖率失真。我们通过分析底层总体评分分布，首次推导出一个守恒律和下界，表明统一校准带来的群体覆盖率偏差无法避免，其规模由跨群体分位数异质性决定。其次，我们证明了共形预测中两种主流公平定义——等覆盖率与等集合大小——存在根本矛盾。第三，我们量化了在群体独立校准与统一校准之间切换的成本。合成数据与真实数据实验均验证了有限样本下同样存在双向权衡。结果表明，在所研究的策略族中，校准选择无法消除群体异质性，只能决定偏差体现在覆盖率还是集合大小上，为实践中面向公平性的校准决策提供了原则性视角。
原文摘要 · Abstract (English)
Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.
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