随机映射的信息损失
The information loss of a stochastic map
摘要：
我们提供了一个随机扩展的Baez-Fritz-Leinster表征的香农信息损失与测量保持功能。这恢复了条件熵和一个密切相关的信息理论度量，我们称之为条件信息损失。虽然不是函子，这些信息措施是半函子，我们介绍的概念，是在任何马尔可夫范畴定义。我们还介绍了一个熵贝叶斯规则的信息措施的概念，我们提供了一个条件熵的表征在这个规则。
英文摘要：
We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we call conditional information loss. Although not functorial, these information measures are semi-functorial, a concept we introduce that is definable in any Markov category. We also introduce the notion of an entropic Bayes' rule for information measures, and we provide a characterization of conditional entropy in terms of this rule.
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。
