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Title
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Rho-tau embedding of statistical models
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Author
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Abstract
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| Two strictly increasing functions ρ and τ determine the rho-tau embedding of a statistical model. The Riemannian metric tensor is derived from the rho-tau divergence. It depends only on the product ρ′τ′ of the derivatives of ρ and τ. Hence, once the metric tensor is fixed still some freedom is left to manipulate the geometry. We call this the gauge freedom. A sufficient condition for the existence of a dually flat geometry is established. It is shown that, if the coordinates of a parametric model are affine then the rho-tau metric tensor is Hessian and the dual coordinates are affine as well. We illustrate our approach using models belonging to deformed exponential families, and give a simple and precise characterization for the rho-tau metric to become Hessian. |
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Language
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English
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Source (book)
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Geometric structures of information / Nielsen, Frank [edit.]
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Source (series)
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Signals and communication technology book series (SCT)
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Publication
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Cham
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Springer
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2018
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ISBN
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978-3-030-02519-9
978-3-030-02520-5
[online]
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DOI
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10.1007/978-3-030-02520-5_1
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Volume/pages
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p. 1-13
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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