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arXiv · 1807.01581

A new class of entropic information measures, formal group theory and information geometry

Miguel A. Rodríguez·Álvaro Romaniega·Piergiulio Tempesta
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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.

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Miguel A. Rodríguez, Álvaro Romaniega, Piergiulio Tempesta. 2018-07-04. A new class of entropic information measures, formal group theory and information geometry. https://doi.org/10.1098/rspa.2018.0633

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