Symmetrizing the Kullback-Leibler Distance

Abstract

We define a new distance measure the resistor-average distance between two probability distributions that is closely related to the Kullback-Leibler distance.While the Kullback-Leibler distance is asymmetric in the two distributions, the resistor-average distance is not.It arises from geometric considerations similar to those used to derive the Chernoff distance.Determining its relation to well-known distance measures reveals a new way to depict how commonly used distance measures relate to each other.