边际有用性：形式化共形预测中的信息差距
Marginally Useful: An Information-Gap Identity in Conformal Prediction
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中文总结 AI 辅助
该研究形式化共形预测中的残差信息差距，指出共形化无法改变该差距，明确共形预测的边际覆盖率非条件、对尖锐度不敏感且需可交换性等关键注意事项。
中文摘要 AI 辅助
共形预测为预测集提供有限样本、与分布无关的边际覆盖率保证，该保证是真实的，但常被误读为预测质量的证据。我们通过一种分解方法将两者区分，称之为残差信息差距：对于单形状残差预测系统，相对于神谕的对数得分遗憾恰好是残差与输入之间的互信息I(R;X)。共形化虽能重新调整覆盖率，但无法改变该量，因为它是预测器形状类的属性，而非校准的属性；任何忽略X的重新校准都无法降低该量。由此引出关于共形预测的常见注意事项：边际覆盖率并非条件覆盖率，有效性对尖锐度不敏感，且该保证需要可交换性。
英文摘要
Conformal prediction has been touted as a more formal, rigorous approach to adding uncertainty to a forecast. The sole objective of this note is to point out that rigor cuts both ways in the case of residual pooling, the technique used in the vast majority of conformal prediction applications. The fact that unconditional guarantee of coverage is provided is not in question, but we make clear, we believe for the first time, that there is an opposing guarantee too: a permanent gambit of logarithmic-score regret which no amount of data or tuning can subsequently reduce. We give the exact size of the sacrifice, and a financial reading of it as the growth rate of an oracle adversary betting against odds set by someone using residual pooling.
