A new class of entropic information measures, formal group theory and information geometry
Abstract
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a large class of entropies. In addition, a method for defining new entropies, using previously known ones with some desired group-theoretical properties is proposed. In the second part of this work, the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied. Finally, a method of constructing new divergences from known ones is discussed; in particular, some results concerning the Riemannian structure associated with the class of divergences under investigation are formulated.
Keywords
Cite
@article{arxiv.1807.01581,
title = {A new class of entropic information measures, formal group theory and information geometry},
author = {Miguel A. Rodríguez and Álvaro Romaniega and Piergiulio Tempesta},
journal= {arXiv preprint arXiv:1807.01581},
year = {2021}
}
Comments
17 pages