关于Csiszár f-发散的Shore和Johnson性质
On Shore and Johnson properties for a Special Case of Csiszár f-divergences
摘要：
幂律分布的重要性归因于这样一个事实，即大多数自然发生的现象都表现出这种分布。虽然指数分布可以通过最小化KL-发散而得到，但某些幂律分布可以通过最小化KL-发散的某些推广（更具体地说，一些Csiszár f-发散的特殊情况）来得到。发散最小化在统计学的信息理论方法中得到了很好的研究。在这项工作中，我们研究的性质最小化的Tsallis分歧，这是一个特殊的情况下，Csiszár f-分歧。与Shore和Johnson（IEEE Trans. IT，1981）的工作一致，我们研究了这些最小化方法所表现出的性质，包括勾股性质。
英文摘要：
The importance of power-law distributions is attributed to the fact that most of the naturally occurring phenomenon exhibit this distribution. While exponential distributions can be derived by minimizing KL-divergence w.r.t some moment constraints, some power law distributions can be derived by minimizing some generalizations of KL-divergence (more specifically some special cases of Csiszár f-divergences). Divergence minimization is very well studied in information theoretical approaches to statistics. In this work we study properties of minimization of Tsallis divergence, which is a special case of Csiszár f-divergence. In line with the work by Shore and Johnson (IEEE Trans. IT, 1981), we examine the properties exhibited by these minimization methods including the Pythagorean property.
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