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• Fisher_information_metric abstract "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. First, it can be understood to be the infinitesimal form of the relative entropy (i.e., the Kullback–Leibler divergence); specifically, it is the Hessian of the divergence. Alternately, it can be understood as the metric induced by the flat space Euclidean metric, after appropriate changes of variable. When extended to complex projective Hilbert space, it becomes the Fubini–Study metric; when written in terms of mixed states, it is the quantum Bures metric.Considered purely as a matrix, it is known as the Fisher information matrix. Considered as a measurement technique, where it is used to estimate hidden parameters in terms of observed random variables, it is known as the observed information.".
• Fisher_information_metric wikiPageExternalLink Feng2009.pdf.
• Fisher_information_metric wikiPageID "488687".
• Fisher_information_metric wikiPageLength "19472".
• Fisher_information_metric wikiPageOutDegree "81".
• Fisher_information_metric wikiPageRevisionID "677120871".
• Fisher_information_metric wikiPageWikiLink 1-form.
• Fisher_information_metric wikiPageWikiLink 2-form.
• Fisher_information_metric wikiPageWikiLink Abuse_of_notation.
• Fisher_information_metric wikiPageWikiLink Arc_length.
• Fisher_information_metric wikiPageWikiLink Berry_phase.
• Fisher_information_metric wikiPageWikiLink Bra–ket_notation.
• Fisher_information_metric wikiPageWikiLink Bures_metric.
• Fisher_information_metric wikiPageWikiLink Category-theoretic.
• Fisher_information_metric wikiPageWikiLink Category:Differential_geometry.
• Fisher_information_metric wikiPageWikiLink Category:Statistical_distance_measures.
• Fisher_information_metric wikiPageWikiLink Category_theory.
• Fisher_information_metric wikiPageWikiLink Cauchy–Schwarz_inequality.
• Fisher_information_metric wikiPageWikiLink Chemical_industry.
• Fisher_information_metric wikiPageWikiLink Cotangent_space.
• Fisher_information_metric wikiPageWikiLink Cramér–Rao_bound.
• Fisher_information_metric wikiPageWikiLink Curve_length.
• Fisher_information_metric wikiPageWikiLink Differentiable_manifold.
• Fisher_information_metric wikiPageWikiLink Discrete_probability_space.
• Fisher_information_metric wikiPageWikiLink Entropy.
• Fisher_information_metric wikiPageWikiLink Euclidean_distance.
• Fisher_information_metric wikiPageWikiLink Euclidean_metric.
• Fisher_information_metric wikiPageWikiLink Expectation_value.
• Fisher_information_metric wikiPageWikiLink Expected_value.
• Fisher_information_metric wikiPageWikiLink Exponential_map_(Riemannian_geometry).
• Fisher_information_metric wikiPageWikiLink Fisher_information.
• Fisher_information_metric wikiPageWikiLink Fisher_information_matrix.
• Fisher_information_metric wikiPageWikiLink Fréchet_space.
• Fisher_information_metric wikiPageWikiLink Fubini–Study_metric.
• Fisher_information_metric wikiPageWikiLink Geodesic.
• Fisher_information_metric wikiPageWikiLink Geometric_phase.
• Fisher_information_metric wikiPageWikiLink Gibbs_measure.
• Fisher_information_metric wikiPageWikiLink Hellinger_distance.
• Fisher_information_metric wikiPageWikiLink Helstrom_metric.
• Fisher_information_metric wikiPageWikiLink Hessian_matrix.
• Fisher_information_metric wikiPageWikiLink Information_geometry.
• Fisher_information_metric wikiPageWikiLink Information_theory.
• Fisher_information_metric wikiPageWikiLink Inner_product.
• Fisher_information_metric wikiPageWikiLink Inner_product_space.
• Fisher_information_metric wikiPageWikiLink Jensen–Shannon_divergence.
• Fisher_information_metric wikiPageWikiLink Kullback–Leibler_divergence.
• Fisher_information_metric wikiPageWikiLink Lagrange_multiplier.
• Fisher_information_metric wikiPageWikiLink Markov_process.
• Fisher_information_metric wikiPageWikiLink Markovian_process.
• Fisher_information_metric wikiPageWikiLink Measure_(mathematics).
• Fisher_information_metric wikiPageWikiLink Measure_space.
• Fisher_information_metric wikiPageWikiLink Mikhail_Gromov_(mathematician).
• Fisher_information_metric wikiPageWikiLink Mikhail_Leonidovich_Gromov.
• Fisher_information_metric wikiPageWikiLink Mixed_state_(physics).
• Fisher_information_metric wikiPageWikiLink Observed_information.
• Fisher_information_metric wikiPageWikiLink One-form.
• Fisher_information_metric wikiPageWikiLink Orientability.
• Fisher_information_metric wikiPageWikiLink Orientable_manifold.
• Fisher_information_metric wikiPageWikiLink Parallel_transport.
• Fisher_information_metric wikiPageWikiLink Partition_function_(mathematics).
• Fisher_information_metric wikiPageWikiLink Polar_coordinate.
• Fisher_information_metric wikiPageWikiLink Polar_coordinate_system.
• Fisher_information_metric wikiPageWikiLink Probability_amplitude.
• Fisher_information_metric wikiPageWikiLink Probability_mass_function.
• Fisher_information_metric wikiPageWikiLink Probability_measure.
• Fisher_information_metric wikiPageWikiLink Probability_space.
• Fisher_information_metric wikiPageWikiLink Process_manufacturing.
• Fisher_information_metric wikiPageWikiLink Processing_industry.
• Fisher_information_metric wikiPageWikiLink Projective_Hilbert_space.
• Fisher_information_metric wikiPageWikiLink Pure_state.
• Fisher_information_metric wikiPageWikiLink Quantum_state.
• Fisher_information_metric wikiPageWikiLink Random_variable.
• Fisher_information_metric wikiPageWikiLink Riemann_manifold.
• Fisher_information_metric wikiPageWikiLink Riemannian_manifold.
• Fisher_information_metric wikiPageWikiLink Riemannian_metric.
• Fisher_information_metric wikiPageWikiLink Ruppeiner_geometry.
• Fisher_information_metric wikiPageWikiLink Ruppeiner_metric.
• Fisher_information_metric wikiPageWikiLink Shunichi_Amari.
• Fisher_information_metric wikiPageWikiLink Sigma-algebra.
• Fisher_information_metric wikiPageWikiLink Sigma_algebra.
• Fisher_information_metric wikiPageWikiLink Simplex.
• Fisher_information_metric wikiPageWikiLink Smooth_manifold.
• Fisher_information_metric wikiPageWikiLink Statistical_manifold.
• Fisher_information_metric wikiPageWikiLink Submanifold.
• Fisher_information_metric wikiPageWikiLink Symplectic_form.
• Fisher_information_metric wikiPageWikiLink Symplectic_vector_space.
• Fisher_information_metric wikiPageWikiLink Tangent_space.
• Fisher_information_metric wikiPageWikiLink Thermodynamic_limit.
• Fisher_information_metric wikiPageWikiLink Two-form.
• Fisher_information_metric wikiPageWikiLink Weinhold_metric.
• Fisher_information_metric wikiPageWikiLinkText "Fisher information metric".
• Fisher_information_metric wikiPageWikiLinkText "Fisher information metric#Relation to Ruppeiner geometry".
• Fisher_information_metric hasPhotoCollection Fisher_information_metric.
• Fisher_information_metric wikiPageUsesTemplate Template:Dubious.
• Fisher_information_metric wikiPageUsesTemplate Template:Reflist.
• Fisher_information_metric subject Category:Differential_geometry.
• Fisher_information_metric subject Category:Statistical_distance_measures.
• Fisher_information_metric hypernym Measures.
• Fisher_information_metric type Physic.
• Fisher_information_metric 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.".

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