Methods of information geometry

By:

Amari, Shun-ichi

Contributor(s):

Series: Translations of mathematical monographs; Vol. 191Publication details: American Mathematical Society, 2000. Providence:Description: x, 206p.; pbk; 25cmISBN:

9780821843024

Subject(s):

DDC classification:

519.5 AMA

Summary: Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the α-connections. The duality between the α-connection and the (−α)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. https://bookstore.ams.org/mmono-191

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	519.5 AMA (Browse shelf(Opens below))	1	Available	031169

includes bibliography and index

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the α-connections. The duality between the α-connection and the (−α)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective.

https://bookstore.ams.org/mmono-191

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