Information Geometry and Its Applications

Information geometry refers to an interdisciplinary field that studies statistics and probability theory by applying the techniques of differential geometry. It investigates statistical manifolds, which are Riemannian manifolds, where each point is a probability distribution. Information geometry offers a differential-geometric structure on manifolds that help in designing and studying statistical decision rules. It has been utilized in a variety of applications such as machine learning, quantum systems, mathematical finance, statistical inference, and neural networks. The amount of information integration within various terminals of a causal dynamical system is measured using information geometry. The amount of information lost can be measured using integrated information when a system is divided into parts and information transmission between the parts is stopped. This book provides comprehensive insights into information geometry and its applications. It presents researches and studies performed by experts across the globe. The book aims to equip students and experts with the advanced topics and upcoming concepts in this area of study.