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arXiv 1706.02686cs.AI
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信念函数相信什么?

What Does a Belief Function Believe In ?

Polish Academy of Sciences(波兰科学院)

Andrzej Matuszewski, Mieczysław A. Kłopotek

摘要:

Dempster-Shafer证据理论中的条件作用已经被Shafer \cite{Shafer:90}定义为通过Dempster规则的信念函数和“事件”的组合。另一方面谢弗\cite{Shafer:90}给出了一个“概率”解释的信念函数(因此间接从一个样本的推导)。鉴于样本导出概率分布的条件概率分布是从子样本(根据条件事件选择)导出的概率分布,本文研究了Dempster组合规则的经验性质。证明了所谓的“条件”信念函数不是给定事件的信念函数,而是给定原始经验数据的信念函数基于此,提出了一种不同于Shafer的信念函数的解释。从数据的信念网络的建设算法推导出这种解释。

英文摘要:

The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule. On the other hand Shafer \cite{Shafer:90} gives a "probabilistic" interpretation of a belief function (hence indirectly its derivation from a sample). Given the fact that conditional probability distribution of a sample-derived probability distribution is a probability distribution derived from a subsample (selected on the grounds of a conditioning event), the paper investigates the empirical nature of the Dempster- rule of combination. It is demonstrated that the so-called "conditional" belief function is not a belief function given an event but rather a belief function given manipulation of original empirical data.\\ Given this, an interpretation of belief function different from that of Shafer is proposed. Algorithms for construction of belief networks from data are derived for this interpretation.

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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