论文标题
hellinger距离的紧密下限，给定的均值和差异
A Tight Lower Bound for the Hellinger Distance with Given Means and Variances
论文作者
论文摘要
在同一2分集中定义的概率度量之间的差异差异具有有趣的属性。对于卡方的差异和相对熵，众所周知，它们的二进制差异分别以给定的均值和方差得出下限。在本说明中，我们表明，平方的二进制差异具有相同的属性，并提出了一个开放的问题，即F-Divergence需要哪些条件才能满足该属性。
The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain lower bounds with given means and variances, respectively. In this note, we show that the binary divergence of the squared Hellinger distance has the same property and propose an open problem that what conditions are needed for f-divergence to satisfy this property.
