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This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern...

From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are...

This is an exciting time. The study of neural networks is enjoying a great renaissance, both in computational neuroscience - the development of information processing models of living brains - and in neural computing - the use of neurally inspired concepts in the construction of "intelligent" machines. Thus the title of this volume, Dynamic Interactions in Neural Networks: Models and Data can be given two interpretations. We present models and data on the dynamic interactions occurring in the brain, and we also exhibit the dynamic interactions between research in computational neuroscience...