Geometry

Download E-books Methods of Information Geometry (Translations of Mathematical Monographs) (Tanslations of Mathematical Monographs) PDF

Info geometry offers the mathematical sciences with a brand new framework of study. It has emerged from the research of the ordinary differential geometric constitution on manifolds of likelihood distributions, which is composed of a Riemannian metric outlined by way of the Fisher info and a one-parameter kin of affine connections known as the $\alpha$-connections. The duality among the $\alpha$-connection and the $(-\alpha)$-connection including the metric play an important function during this geometry. this type of duality, having emerged from manifolds of chance distributions, is ubiquitous, showing in quite a few difficulties which would don't have any particular relation to chance idea. in the course of the duality, it's attainable to investigate a number of basic difficulties in a unified viewpoint. the 1st half this ebook is dedicated to a finished creation to the mathematical origin of knowledge geometry, together with preliminaries from differential geometry, the geometry of manifolds or likelihood distributions, and the overall concept of twin affine connections. the second one half the textual content presents an outline of many components of purposes, akin to facts, linear platforms, details idea, quantum mechanics, convex research, neural networks, and affine differential geometry. The e-book can function an appropriate textual content for a subject matters direction for complicated undergraduates and graduate scholars. This quantity is co-published by means of the AMS and Oxford college Press. The AMS has unique distribution rights in North the USA. AMS individuals in Europe may perhaps buy the ebook from the AMS. either the AMS and OUP have all over the world distribution rights.

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