提出更严格的校准标准，让预测在所有合理评分规则下都更准确。
Proper Calibeating
- 定义新概念：在所有合理评分规则下统一校准
- 证明传统校准能保证新标准，但反向不成立
- 给出确保新标准的方法，适合做可靠预测的研究者
经典校准概念及其近期改进‘校准胜出’（calibeating）原本基于标准二次评分规则。本文将其推广至所有‘恰当’评分规则（即最优预测为真实分布），定义了‘恰当校准’与‘恰当校准胜出’，要求误差在所有有界恰当评分规则下一致收敛至零。首先证明校准恒蕴含恰当校准，但校准胜出未必蕴含恰当校准；其次，给出保证恰当校准胜出及多维度恰当校准胜出的构造方法；最后，揭示恰当校准等价于在不确定决策中对预测做出最优回应时的普遍无悔性。
原文摘要 · Abstract (English)
The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which the best forecast is the true distribution) and define $\textit{proper-calibration}$ and $\textit{proper-calibeating}$ by requiring the errors to converge to zero uniformly over all bounded proper scoring rules. We first establish that calibration always implies proper-calibration, whereas calibeating need not imply proper-calibeating. Second, we show how to guarantee proper-calibeating and proper-multicalibeating. Finally, we demonstrate the equivalence between proper-calibration and universal no regret when best replying to forecasts in decision-making under uncertainty.
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