Hessian Structures on Deformed Exponential Families
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.
KeywordsHessian manifold statistical manifold deformed exponential family divergence information geometry
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