Hessian Structures on Deformed Exponential Families

  • Hiroshi Matsuzoe
  • Masayuki Henmi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8085)


A deformed exponential family is a generalization of exponential families. It is known that an exponential family naturally has dualistic Hessian structures, and its canonical divergence coincides with the Kullback-Leibler divergence, which is also called the relative entropy. On the other hand, a deformed exponential family naturally has two kinds of dualistic Hessian structures. In this paper, such Hessian structures are summarized and a generalized relative entropy is constructed from the viewpoint of estimating functions.


Hessian manifold statistical manifold deformed exponential family divergence information geometry 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hiroshi Matsuzoe
    • 1
  • Masayuki Henmi
    • 2
  1. 1.Department of Computer Science and Engineering, Graduate School of EngineeringNagoya Institute of TechnologyShowa-kuJapan
  2. 2.The Institute of Statistical MathematicsTachikawaJapan

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