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001435211 001__ 1435211
001435211 003__ OCoLC
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001435211 019__ $$a1242027356
001435211 020__ $$a9783030654597$$q(electronic bk.)
001435211 020__ $$a3030654591$$q(electronic bk.)
001435211 020__ $$z9783030654580
001435211 020__ $$z3030654583
001435211 0247_ $$a10.1007/978-3-030-65459-7$$2doi
001435211 035__ $$aSP(OCoLC)1243544872
001435211 040__ $$aEBLCP$$beng$$erda$$epn$$cEBLCP$$dYDX$$dEBLCP$$dGW5XE$$dOCLCO$$dOCLCF$$dUKAHL$$dOCLCQ$$dOCLCO$$dCOM$$dOCLCQ
001435211 049__ $$aISEA
001435211 050_4 $$aQA613
001435211 08204 $$a516/.07$$223
001435211 24500 $$aProgress in information geometry :$$btheory and applications /$$cFrank Nielsen, editor.
001435211 264_1 $$aCham :$$bSpringer,$$c[2021]
001435211 300__ $$a1 online resource (282 pages)
001435211 336__ $$atext$$btxt$$2rdacontent
001435211 337__ $$acomputer$$bc$$2rdamedia
001435211 338__ $$aonline resource$$bcr$$2rdacarrier
001435211 4901_ $$aSignals and communication technology
001435211 5050_ $$aIntro -- Preface -- Contents -- 1 Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities -- 1.1 Introduction -- 1.2 Statistical Bundle Modelled on Orlicz Spaces -- 1.2.1 Orlicz Spaces -- 1.2.2 Calculus of the Gaussian Space -- 1.2.3 Exponential Statistical Bundle -- 1.3 Bounding the Orlicz Norm with the Orlicz Norm of the Gradient -- 1.3.1 Ornstein-Uhlenbeck Semi-group -- 1.3.2 Generator of the Ornstein-Uhlenbeck Semi-group -- 1.4 Discussion and Conclusions -- 1.4.1 Sub-exponential Random Variables -- 1.4.2 Hyvärinen Divergence -- 1.4.3 Otto's Metric
001435211 5058_ $$a3 Affine Connections with Torsion in (Para- )complexified Structures -- 3.1 Introduction -- 3.2 Torsion of and Integrability of L -- 3.2.1 L Conjugation of -- 3.2.2 Nijenhuis Tensor NL and Integrability -- 3.2.3 MC1 Versus MC2 -- 3.3 Torsion of Under (Para- )complexification -- 3.3.1 Splitting of TmathcalMotimesmathbbL by L -- 3.3.2 (Para- )holomorphicity of -- 3.3.3 (Para- )complexifying NL and T -- 3.3.4 Torsion-Compatibility (MC1) -- 3.3.5 Torsion-Coupling (MC2) -- 3.4 Summary and Discussions -- References
001435211 5058_ $$a4 Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations -- 4.1 Introduction -- 4.2 Underlying Geometry -- 4.2.1 Para-Contact Metric Manifolds -- 4.2.2 Contact Manifold -- 4.2.3 Legendre Submanifold as Dually Flat Space -- 4.2.4 Legendre Submanifold as Attractor -- 4.3 Distribution Functions from Solvable Master Equations -- 4.3.1 Denormalization -- 4.4 Observables with Solvable Master Equations -- 4.5 Geometric Description of Master Equations -- 4.5.1 Geometry of Equilibrium States
001435211 5058_ $$a4.5.2 Geometry of Nonequilibrium States -- 4.6 Geometric Description of Expectation Variables -- 4.6.1 Geometry of Equilibrium States -- 4.6.2 Geometry of Nonequilibrium States -- 4.7 Beyond the Toy Model -- 4.7.1 Equilibrium States -- 4.7.2 Nonequilibrium States -- 4.8 Conclusions -- References -- 5 Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures -- 5.1 Preamble -- 5.2 Invariant Koszul Form for Homogeneous Bounded Domains -- 5.3 Contextualization with Last Advanced Works -- 5.4 Koszul Hessian Geometric Structure of Information Geometry
001435211 506__ $$aAccess limited to authorized users.
001435211 520__ $$aThis book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI2019 Geometric Science of Information that was held at ENAC, Toulouse (France).
001435211 588__ $$aDescription based on print version record.
001435211 650_0 $$aManifolds (Mathematics)
001435211 650_6 $$aVariétés (Mathématiques)
001435211 655_0 $$aElectronic books.
001435211 7001_ $$aNielsen, Frank,$$eeditor.
001435211 77608 $$iPrint version:$$aNielsen, Frank.$$tProgress in Information Geometry.$$dCham : Springer International Publishing AG, ©2021$$z9783030654580
001435211 830_0 $$aSignals and communication technology.
001435211 852__ $$bebk
001435211 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-65459-7$$zOnline Access$$91397441.1
001435211 909CO $$ooai:library.usi.edu:1435211$$pGLOBAL_SET
001435211 980__ $$aBIB
001435211 980__ $$aEBOOK
001435211 982__ $$aEbook
001435211 983__ $$aOnline
001435211 994__ $$a92$$bISE