Title :
On the chi square and higher-order chi distances for approximating f-divergences
Author :
Nielsen, Frank ; Nock, Richard
Author_Institution :
Sony Comput. Sci. Labs., Inc., Tokyo, Japan
Abstract :
We report closed-form formula for calculating the Chi square and higher-order Chi distances between statistical distributions belonging to the same exponential family with affine natural space, and instantiate those formula for the Poisson and isotropic Gaussian families. We then describe an analytic formula for the f-divergences based on Taylor expansions and relying on an extended class of Chi-type distances.
Keywords :
Gaussian processes; stochastic processes; Chi-type distances; Poisson families; Taylor expansions; affine natural space; chi square; closed-form formula; divergence approximation; f-divergences; higher-order Chi distances; higher-order chi distances; isotropic Gaussian families; statistical distributions; Approximation methods; Density measurement; Generators; Materials; Power measurement; Taylor series; Chi square distance; Kullback–Leibler divergence; Taylor series; exponential families; statistical divergences;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2013.2288355
