Year: 2019
Type: preprint
Abstract: We show that the $f$-divergence between any two densities of potentially different location-scale families can be reduced to the calculation of the $f$-divergence between one standard density with another location-scale density. It follows that the $f$-divergence between two scale densities depends only on the scale ratio. We then report conditions on the standard distribution to get symmetric $f$-divergences: First, we prove that all $f$-divergences between densities of a location family are symmetric whenever the standard density is even, and second, we illustrate a generic symmetric property with the calculation of the Kullback-Leibler divergence between scale Cauchy distributions. Finally, we show that the minimum $f$-divergence of any query density of a location-scale family to another location-scale family is independent of the query location-scale parameters.
Source: arXiv (Cornell University)
Author: Nielsen, Frank
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2941243960