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.

翻译：在同一两点上定义的概率计量方法之间的二进制差异是两进制差异,两者间的差异具有有趣的属性。对于奇差的差数和相对的倍数,已知它们的二进制差异分别以特定手段和差异达到较低的界限。在本说明中,我们表明平方海灵格距离的二进制差异具有相同的属性,并提出了一个尚未解决的问题,即满足这一属性需要什么样的条件。