Computational Information Geometry | Frank NIELSEN

Computational Information Geometry

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The field of computational information geometry (discrete information geometry) is interested in exploring the following domains:
Let us give some examples of information manifolds: Strictly speaking, geometrizing information-theoretic problems does not provide a more powerful framework in theory. This is because synthetical and analytical geometries are equivalent. Informally, that means that we can do geometry by algebraic equations. However, geometrizing problems help grab intuition on the problem at hand. Geometry also yields novel notions to mathematical theories. For example, let us cite the two curvature notions in statistics: exponential and mixture curvatures emanating from conjugate connections. So although synthetical geometry provides the same power as analytical geometry, the third-order asymptotic theory of statistics has been obtained so far only from synthetical information geometry. Dual differential geometries are also useful to tackle information-theoretic problems such as

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International Workshop on Matrices and Statistics (with historical note
Online December 2007. Last updated, January 2010. (c) Frank NIELSEN, All rights reserved.