关于相对$α$ -熵和Rényi发散中投影的等价性
On The Equivalence of Projections In Relative $α$-Entropy and Rényi Divergence
摘要：
本工作的目的是建立两个最近发表的投影定理，一个处理相对熵的参数化推广，另一个处理雷尼发散，是等价的概率测度空间上的对应关系。此外，我们证明了相关的“毕达哥拉斯”定理是等价的，根据这种对应关系。最后，我们申请江口的方法获得黎曼度量从一般的发散函数，以表明上述发散所产生的几何是等价的上述对应关系。
英文摘要：
The aim of this work is to establish that two recently published projection theorems, one dealing with a parametric generalization of relative entropy and another dealing with Rényi divergence, are equivalent under a correspondence on the space of probability measures. Further, we demonstrate that the associated "Pythagorean" theorems are equivalent under this correspondence. Finally, we apply Eguchi's method of obtaining Riemannian metrics from general divergence functions to show that the geometry arising from the above divergences are equivalent under the aforementioned correspondence.
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