从信息论角度重新审视概率分布否定，证明其合理性与普适性
An Information Theoretic Treatment of Yager's Probability Distribution Negation
- 基于信息论与排序理论，统一分析Yager的分布否定方法
- 揭示该否定在多种信息准则下具有最优性质
- 适合对概率推理与不确定性建模感兴趣的学者
在经典论文（Yager 2015）中，Yager定义了概率分布 $\mathbf{p}=(p_1,\dots,p_n)$ 的否定为 $\overline{\mathbf{p}} = (\overline{p}_1,\dots,\overline{p}_n)$，其中 $\overline{p}_i = (1-p_i)/(n-1)$，$i=1,\ldots,n$。本文对该否定及其推广进行系统的信息论分析。利用信息论与序理论工具，我们在统一框架下推广并强化了此前已知的多项性质。总体而言，结果为Yager否定在各类信息论准则下的自然性与原则性提供了有力理论支持。
原文摘要 · Abstract (English)
In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution $\mathbf{p}=(p_1,\dots,p_n)$, as the distribution $\overline{\mathbf{p}} = (\overline{p}_1,\dots,\overline{p}_n)$, where $\overline{p}_i = ({1-p_i})/({n-1}),$ for $ i=1, \ldots , n.$ In this paper, we present a comprehensive information-theoretic analysis of Yager's negation and its generalizations. Using tools from information theory and majorization theory, we unify, extend, and strengthen a number of previously known properties of Yager's negation within a common framework. Overall, our results offer strong theoretical justification for Yager's negation as the most natural and principled definition of probability distribution negation under various information theoretic criteria.
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