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arXiv 2203.09852cs.LG
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错误校准下的决策

Decision-Making under Miscalibration

Weizmann Institute of Science(魏茨曼科学研究所)

Guy N. Rothblum, Gal Yona

摘要:

基于ML的预测用于为有关个人的后续决策提供信息。我们应该如何使用预测(例如,心脏病发作的风险)以通知下游二元分类决策(例如,(一)医疗过程?当风险估计被完美地校准时,答案是很好理解的:分类问题的成本结构导致最佳治疗阈值$j^{\star}$。然而,在实践中,一定程度的错误校准是不可避免的,这就提出了一个基本问题:如何使用潜在的错误校准预测来为二元决策提供信息?我们形式化一个自然的(无分布)解决方案的概念:鉴于预期的误校准的$α$,我们建议使用阈值$j$,最大限度地减少最坏情况下的遗憾,所有$α$ -误校准的预测,其中遗憾是使用阈值之间的差异,在临床效用的问题,并在事后使用最佳阈值。当使用预期和最大校准误差测量误校准时,我们提供了$j$的封闭形式表达式,这表明它确实不同于$j^{\star}$(完美校准下的最佳阈值)。我们验证了我们的理论研究结果的真实数据,表明有自然的情况下,使用$j$决策提高了临床效用。

英文摘要:

ML-based predictions are used to inform consequential decisions about individuals. How should we use predictions (e.g., risk of heart attack) to inform downstream binary classification decisions (e.g., undergoing a medical procedure)? When the risk estimates are perfectly calibrated, the answer is well understood: a classification problem's cost structure induces an optimal treatment threshold $j^{\star}$. In practice, however, some amount of miscalibration is unavoidable, raising a fundamental question: how should one use potentially miscalibrated predictions to inform binary decisions? We formalize a natural (distribution-free) solution concept: given anticipated miscalibration of $α$, we propose using the threshold $j$ that minimizes the worst-case regret over all $α$-miscalibrated predictors, where the regret is the difference in clinical utility between using the threshold in question and using the optimal threshold in hindsight. We provide closed form expressions for $j$ when miscalibration is measured using both expected and maximum calibration error, which reveal that it indeed differs from $j^{\star}$ (the optimal threshold under perfect calibration). We validate our theoretical findings on real data, demonstrating that there are natural cases in which making decisions using $j$ improves the clinical utility.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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