Oct 12, 2010

Statistical manifold: Dual conjugate connections

Post @ 23:05:06 | Differential geometry

Conjugate connections play a crucial role in information geometry. For dually flat statistical spaces, we have the exponential and mixture connections that are dual to each other. There have been several ways to define what we mean by a statistical manifold. The following paper summarizes the various approaches nicely.

Conjugate connections on statistical manifolds S. E. Stepanov, E. S. Stepanova and I. G. Shandra

It refers to a 1945 russian paper examining dual connections.

A. P. Norden,
On Pairs of Conjugate Parallel Displacements in Multidimensional Spaces,
Dokl. Akad. Nauk SSSR 49 (9), 1345-1347 (1945).


Frank.

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2 Comments

Re: Statistical manifold: Dual conjugate connections

BTW, mathnet.ru is pretty good for finding Russian math papers. Search for Norden gives 72 results, all of them seem to be available as pdf's. This paper looks similar to the one cited, "Parallel Transport of Dual Vectors"
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=uzku&paperid=379&option_lang=rus

Re: Statistical manifold: Dual conjugate connections

Excellent. One more reason to get russian basics. Thanks for the link. Frank.

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