Methods of Information Geometry

There has been strong progress in the field of information geometry in recent years and yet there are few textbooks which reflect these developments, except for those which deal with statistics. Information geometry provides a new method applicable to various areas including information sciences and physical sciences. It has emerged from investigating the geometrical structures of the manifold of probability distributions, and has been applied successfully to statistical inference problems. However, it has been proved that information geometry opens a new paradigm useful for elucidation of information systems, intelligent systems, physical systems and mathematical systems. Information geometry has become one of the fundamental methods of analyzing neurocomputing and related areas. Its usefulness has also been recognized in multiterminal information theory and portfolio, in nonlinear systems and nonlinear prediction, in mathematical programming, in statistical inference and information theory of quantum mechanical systems, and so on. Its mathematical foundations have also shown a remarkable progress.
The first three chapters of the book provide a comprehensive introduction to the mathematical foundation of information geometry while the remaining chapters provide an overview of the scope of its application. It is hoped that Methods of Information Geometry will become a key text in information geometry and help to inspire further developments in the field.