Abstract
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.
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Matsuzoe, H., Henmi, M. (2013). Hessian Structures on Deformed Exponential Families. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_29
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DOI: https://doi.org/10.1007/978-3-642-40020-9_29
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