An Elementary Introduction to Information Geometry
Frank Nielsen
Abstract
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.
Topics & Concepts
Information geometryMathematical proofExposition (narrative)Differential geometrySynthetic geometryDifferential (mechanical device)MathematicsGeometric analysisComputer scienceGeometryAlgebra over a fieldCalculus (dental)Pure mathematicsProjective geometryDifferential equationMathematical analysisPhysicsOrdinary differential equationThermodynamicsScalar curvatureArtCurvatureDifferential algebraic equationMedicineLiteratureDentistryTopological and Geometric Data AnalysisRough Sets and Fuzzy LogicBayesian Modeling and Causal Inference