[论文] Truthful Calibration Measures for Sequential Prediction

论文概要

研究领域: ML 作者: Anagha Gokul, Jason Hartline, Lunjia Hu, Jonathan Ullman, Yifan Wu 发布时间: 2026-08-21 arXiv: 2608.21348

中文摘要

校准要求概率报告在条件上无偏，并可靠地解释为概率。校准度量将数值误差分配给未校准的报告。Haghtalab等人（2024）提出了一种近似真实的在线预测校准度量，留下精确真实性是否与完备性和可靠性相容的开放问题。我们对顺序二元预测否定地回答了这个问题：精确真实性与完备性和可靠性不相容，即使对于独立结果也是如此。然后我们证明这一不可能性特定于精确真实性。我们给出两种从基础校准度量产生加性和乘性近似真实校准度量的一般归约。应用乘性归约，对于每个0 < ε < 1，我们构造了一个可靠且完备的校准度量，它是(1+exp(-T^(1-ε)/2/2))-乘性真实的。这改进了Haghtalab等人（2024）的近似真实性保证。

原文摘要

Calibration requires probabilistic reports to be conditionally unbiased and reliably interpretable as probabilities. A calibration measure assigns numerical error to miscalibrated reports. Haghtalab et al. (2024) proposed an approximately truthful calibration measure for online prediction, leaving open whether exact truthfulness is compatible with completeness and soundness. We resolve this question negatively for sequential binary prediction: exact truthfulness is incompatible with completeness and soundness, even for independent outcomes. We then show that this impossibility is specific to exact truthfulness. We give two general reductions from a base calibration measure, producing additively and multiplicatively approximately truthful calibration measures, respectively. Applying the mul...

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