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Dually affine Information Geometry modeled on a Banach space
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In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting.
Forward citations
Cited by 2 Pith papers
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Affine calculus for constrained minima of the Kullback-Leibler divergence
A geometric calculus using exponential and mixture coordinates is applied to derive natural gradients for KL-type divergences in mean-field, transport, GAN, and variational Bayes settings.
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Information geometry of Bayes computations
In nonparametric information geometry, marginalization and conditioning in Bayes computations are realized as derivatives of maps between statistical bundles.
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