geometry induced by a generalization of rényi divergence
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ID: 173220
2016
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Abstract
In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a φ-function, the same function that is used in the definition of non-parametric φ-families. The properties of φ-functions proved to be crucial in the generalization of Rényi divergence. Assuming appropriate conditions, we verify that the generalized Rényi divergence reduces, in a limiting case, to the φ-divergence. In generalized statistical manifold, the φ-divergence induces a pair of dual connections D ( − 1 ) and D ( 1 ) . We show that the family of connections D ( α ) induced by the generalization of Rényi divergence satisfies the relation D ( α ) = 1 − α 2 D ( − 1 ) + 1 + α 2 D ( 1 ) , with α ∈ [ − 1 , 1 ] .
| Reference Key |
souza2016entropygeometry
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|---|---|
| Authors | ;David C. de Souza;Rui F. Vigelis;Charles C. Cavalcante |
| Journal | European journal of medicinal chemistry |
| Year | 2016 |
| DOI |
10.3390/e18110407
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| URL | |
| Keywords | Keywords not found |
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