An Elementary Introduction to Information Geometry

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity. By analogy to Information Theory (IT), which considers primarily the communication of messages over noisy transmission channels, we define Information Sciences (IS) as the fields that study communication between noisy data and families of models. Information sciences encompass information theory and also include Probability and Statistics, Machine Learning, and Artificial Intelligence. We review key milestones of information geometry and report various definitions of the field put forward by its pioneers, thereby providing a modern view of the basic structures inherent to Information Geometry.