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Review

An Elementary Introduction to Information Geometry

Sony Computer Science Laboratories, Tokyo 141-0022, Japan
Entropy 2020, 22(10), 1100; https://doi.org/10.3390/e22101100
Received: 6 September 2020 / Revised: 25 September 2020 / Accepted: 27 September 2020 / Published: 29 September 2020
(This article belongs to the Special Issue Review Papers for Entropy)
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. View Full-Text
Keywords: differential geometry; metric tensor; affine connection; metric compatibility; conjugate connections; dual metric-compatible parallel transport; information manifold; statistical manifold; curvature and flatness; dually flat manifolds; Hessian manifolds; exponential family; mixture family; statistical divergence; parameter divergence; separable divergence; Fisher–Rao distance; statistical invariance; Bayesian hypothesis testing; mixture clustering; α-embeddings; mixed parameterization; gauge freedom differential geometry; metric tensor; affine connection; metric compatibility; conjugate connections; dual metric-compatible parallel transport; information manifold; statistical manifold; curvature and flatness; dually flat manifolds; Hessian manifolds; exponential family; mixture family; statistical divergence; parameter divergence; separable divergence; Fisher–Rao distance; statistical invariance; Bayesian hypothesis testing; mixture clustering; α-embeddings; mixed parameterization; gauge freedom
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MDPI and ACS Style

Nielsen, F. An Elementary Introduction to Information Geometry. Entropy 2020, 22, 1100. https://doi.org/10.3390/e22101100

AMA Style

Nielsen F. An Elementary Introduction to Information Geometry. Entropy. 2020; 22(10):1100. https://doi.org/10.3390/e22101100

Chicago/Turabian Style

Nielsen, Frank. 2020. "An Elementary Introduction to Information Geometry" Entropy 22, no. 10: 1100. https://doi.org/10.3390/e22101100

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