About: Fisher information metric

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In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space. It can be used to calculate the informational difference between measurements. The metric is interesting in several respects. By Chentsov’s theorem, the Fisher information metric on statistical models is the only Riemannian metric (up to rescaling) that is invariant under sufficient statistics.

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rdf:type	yago:WikicatStatisticalDistanceMeasures yago:Abstraction100002137 yago:Act100030358 yago:Action100037396 yago:Choice100161243 yago:Decision100162632 yago:Event100029378 yago:Maneuver100168237 yago:Measure100174412 yago:Move100165942 yago:PsychologicalFeature100023100 yago:YagoPermanentlyLocatedEntity
rdfs:label	Fisher information metric (en) Информационная метрика Фишера (ru)
rdfs:comment	In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space. It can be used to calculate the informational difference between measurements. The metric is interesting in several respects. By Chentsov’s theorem, the Fisher information metric on statistical models is the only Riemannian metric (up to rescaling) that is invariant under sufficient statistics. (en) Информационная метрика Фишера в — это особая риманова метрика, которая может быть определена на гладком , то есть на гладком многообразии, точки которого являются вероятностными мерами из общего вероятностного пространства. Ее можно использовать для расчета информационной разницы между измерениями. Метрика интересна в нескольких отношениях. По теореме Ченцова, информационная метрика Фишера на статистических моделях является единственной (с точностью до масштабирования) римановой метрикой, инвариантной при достаточной статистике. (ru)
dcterms:subject	Statistical distance Differential geometry Information geometry
Wikipage page ID	488687 (xsd:integer)
Wikipage revision ID	1048658690 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability amplitude Probability space Euclidean metric Bra–ket notation Statistical distance Information geometry Sigma algebra Differential geometry Measure theory Information geometry Chemical industry Geometric phase Statistical manifold Entropy Fréchet space Geodesic Gibbs measure Submanifold Shun'ichi Amari Simplex Fubini–Study metric Hellinger distance Partition function (mathematics) Tangent space Measure space Cauchy–Schwarz inequality Weak topology Action (physics) Exponential map (Riemannian geometry) Fisher information matrix Parallel transport Cauchy sequence Radon–Nikodym derivative Projective Hilbert space Random variable Riemannian manifold Riemannian metric Hilbert space Cotangent space Cramér–Rao bound Jensen–Shannon divergence Abuse of notation Chentsov’s theorem Lagrange multiplier Hessian matrix Bures metric Square-integrable Pure state Information theory Inner product Kullback–Leibler divergence Radon–Nikodym theorem Helstrom metric Orientable manifold Smooth manifold Observed information Fisher information Probability measure Sufficient statistic Ruppeiner metric 2-form Radon–Nikodym property Symplectic form Category-theoretic Discrete probability space Mixed state (physics) Polar coordinate Markovian process Mikhail Gromov (mathematician) Processing industry 1-form Berry phase Curve length Expectation value Weinhold metric
Link from a Wikipage to an external page	https://arxiv.org/pdf/1310.7780.pdf
sameAs	Fisher information metric Fisher information metric Fisher information metric

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