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An Elementary Introduction to Information Geometry
review-article
29 September 2020
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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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.
Related collections
Most cited references160
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Natural Gradient Works Efficiently in Learning
Shun-ichi Amari (1998)
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Author and article information
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