An Elementary Introduction to Information Geometry
Copyright policy )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.
FOS: Computer and information sciences, Computer Science - Machine Learning, mixture clustering, Science, QC1-999, Computer Science - Information Theory, Hessian manifolds, gauge freedom, Machine Learning (stat.ML), Review, statistical manifold, Astrophysics, Machine Learning (cs.LG), Bayesian hypothesis testing, dual metric-compatible parallel transport, Statistics - Machine Learning, exponential family, mixture family, conjugate connections, affine connection, Fisher–Rao distance, differential geometry, statistical invariance, information manifold, Physics, Information Theory (cs.IT), Q, α-embeddings, mixed parameterization, dually flat manifolds, QB460-466, statistical divergence, curvature and flatness, parameter divergence, metric tensor, metric compatibility, separable divergence
FOS: Computer and information sciences, Computer Science - Machine Learning, mixture clustering, Science, QC1-999, Computer Science - Information Theory, Hessian manifolds, gauge freedom, Machine Learning (stat.ML), Review, statistical manifold, Astrophysics, Machine Learning (cs.LG), Bayesian hypothesis testing, dual metric-compatible parallel transport, Statistics - Machine Learning, exponential family, mixture family, conjugate connections, affine connection, Fisher–Rao distance, differential geometry, statistical invariance, information manifold, Physics, Information Theory (cs.IT), Q, α-embeddings, mixed parameterization, dually flat manifolds, QB460-466, statistical divergence, curvature and flatness, parameter divergence, metric tensor, metric compatibility, separable divergence
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