序列预测的真实校准度量
Truthful Calibration Measures for Sequential Prediction
- Khoury College of Computer Sciences（科里计算机科学学院）
- Northeastern University（东北大学）
- Northwestern University（西北大学）
- Microsoft Research（微软研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究序列二元预测中完全真实性与校准度量的兼容性，证明完全真实性与完备性、可靠性不兼容，提出两种归约构造近似真实校准度量，改进了已有近似真实性保证。
AI中文摘要：
校准要求概率报告具有条件无偏性，且可可靠地解释为概率。校准度量会对未校准的报告赋予数值误差。Haghtalab等人（2024）提出了一种适用于在线预测的近似真实校准度量，但留下了一个开放问题：完全真实性是否与完备性和可靠性兼容。我们针对序列二元预测否定了该问题：即使对于独立结果，完全真实性也与完备性和可靠性不兼容。随后我们表明，这种不可能性仅针对完全真实性。我们给出了从基础校准度量出发的两种通用归约，分别产生加性和乘性近似真实校准度量。应用乘性归约，对于每个0<ε<1，我们构造了一种可靠且完备的校准度量，其为(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。
英文摘要：
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 multiplicative reduction, for every $0 < \varepsilon < 1$ we construct a sound and complete calibration measure that is $(1+\exp(-T^{(1-\varepsilon)/2}/2))$-multiplicatively truthful. This improves the approximate-truthfulness guarantee of Haghtalab et al. (2024).
