Authors:Shun-Ichi Amari, Hiroshi Nagaoka,
Publisher: American Mathematical Society
Keywords: mathematical, monographs, tanslations, translations, information, geometry, methods
Number of Pages: 206
Published: 2007-04-13
List price: $79.00
ISBN-10: 0821843028
ISBN-13: 9780821843024

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 $alpha$-connections. The duality between the $alpha$-connection and the $(-alpha)$-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiq