Quasi-arithmetic Centers, Quasi-arithmetic Mixtures, and the Jensen-Shannon-Divergences

Author

Nielsen, Frank

Abstract

We first explain how the information geometry of Bregman manifolds brings a natural generalization of scalar quasi-arithmetic means that we term quasi-arithmetic centers. We study the invariance and equivariance properties of quasi-arithmetic centers from the viewpoint of the Fenchel-Young canonical divergences. Second, we consider statistical quasi-arithmetic mixtures and define generalizations of the Jensen-Shannon divergence according to geodesics induced by affine connections.