Publication: A new class of entropic information measures, formal group theory and information geometry.
Loading...
Official URL
Full text at PDC
Publication Date
2019-02
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Royal soc
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.
Description
© 2019 Royal society.
M.A.R. has been partly supported by the research project no. FIS2015-63966, MINECO, Spain. P.T. has been partly supported by the research project FIS2015-63966, MINECO, Spain, by the ICMAT Severo Ochoa grant no. SEV-2015-0554 and by the GNFM, Italy.