研究模糊概率下可诱导属性的条件，为鲁棒优化提供理论支持。
Property Elicitation on Imprecise Probabilities
- 提出模糊概率下属性诱导的充要条件
- 发现最大贝叶斯风险对应的概率决定可诱导属性
- 适用于分布鲁棒优化与多分布学习场景
属性诱导研究哪些概率分布的特征可通过最小化风险来确定。本文将属性诱导推广至模糊概率（IP）情形，其动机源于分布鲁棒优化和多分布学习。这两类框架将单个精确概率下的风险最小化，替换为在一组概率上的最大-最小风险最小化——即模糊概率。本文给出了模糊概率属性可诱导性的必要与充分条件。核心发现是：所诱导的模糊概率属性，等价于该模糊概率集中具有最大贝叶斯风险的概率所对应的经典属性。
原文摘要 · Abstract (English)
Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by distributionally robust optimization and multi-distribution learning. Both those frameworks replace the minimization of a single risk over a (precise) probability by a maximin risk minimization over a set of probabilities -- i.e. an IP. We show what can be learned in those multi-distribution setups by providing necessary and sufficient conditions for the elicitability of an IP-property. Central to these conditions is the observation made in related literature that the elicited IP-property is the corresponding classical property of the probability in the IP with the maximum Bayes risk.
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