Dual Connections in Nonparametric Classical Information Geometry
نویسنده
چکیده
We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We also define the α-connections and prove that they are convex mixtures of the extremal (±1)-connections.
منابع مشابه
Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds
Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint a...
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تاریخ انتشار 2005