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2016 PKU Mini-Course: Information Geometry

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Advertisement Hide. Methods of Information Geometry to model complex shapes. Authors Authors and affiliations A. De Sanctis S. Part of the following topical collections: Mathematical Modeling of Complex Systems.

Methods of Information Geometry to model complex shapes | SpringerLink

This is a preview of subscription content, log in to check access. Amari, H. Nagaoka, Methods of Information Geometry , Vol.

Bertuglia, F. Bookstein, Stat.

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Dryden, K. Classically, information geometry considered a parametrized statistical model as a Riemannian manifold.


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For such models, there is a natural choice of Riemannian metric, known as the Fisher information metric. In the special case that the statistical model is an exponential family , it is possible to induce the statistical manifold with a Hessian metric i.

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In this case, the manifold naturally inherits two flat affine connections , as well as a canonical Bregman divergence. Historically, much of the work was devoted to studying the associated geometry of these examples.

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In the modern setting, information geometry applies to a much wider context, including non-exponential families, nonparametric statistics , and even abstract statistical manifolds not induced from a known statistical model. The results combine techniques from information theory , affine differential geometry , convex analysis and many other fields. The history of information geometry is associated with the discoveries of at least the following people, and many others.

From Wikipedia, the free encyclopedia. This article may need to be rewritten to comply with Wikipedia's quality standards , as This should be edited to include some statistical background.. You can help.