论文标题
存在RényiDivergence的概括的条件
Conditions for the existence of a generalization of Rényi divergence
论文作者
论文摘要
我们为存在RényiDivergence的概括提供了必要的条件，该条件是根据变形指数函数定义的。如果基本量度$μ$是非原子的，我们发现并非所有变形的指数函数都可以用于RényiDivergence的概括中。提供涉及变形指数函数的条件。在$μ$的情况下，纯原子（对自然数的计数量度），我们表明任何变形的指数函数都可以在概括中使用。
We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $μ$ is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case $μ$ is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.
