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Progress in information geometrytheo...

Nielsen, Frank.

Progress in information geometrytheory and applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Progress in information geometryedited by Frank Nielsen.
其他題名:	theory and applications /
其他作者:	Nielsen, Frank.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xii, 274 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Manifolds (Mathematics)
電子資源:	https://doi.org/10.1007/978-3-030-65459-7
ISBN:	9783030654597$q(electronic bk.)

Progress in information geometrytheory and applications /
Progress in information geometrytheory and applications /[electronic resource] :edited by Frank Nielsen. - Cham :Springer International Publishing :2021. - xii, 274 p. :ill., digital ;24 cm. - Signals and communication technology,1860-4862. - Signals and communication technology..

Information Geometry of smooth densities on the Gaussian space: Poincare inequalities -- On Normalization Functions and ϕ-families of Probability Distributions -- Affine Connections with Torsion in (para-)complexified Structures -- Contact Hamiltonian systems for probability distribution functions and expectation variables: A study based on a class of master equations -- Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures -- Gauge freedom of entropies on q-Gaussian measures -- On geodesic triangles with right angles in a dually flat space -- Chain Rule Optimal Transport -- Towards the "Shape" of Cosmological Observables and the String Theory Landscape with Topological Data Analysis -- A review of two decades of correlations, hierarchies, networks and clustering in financial markets.

This 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 GSI'2019 - Geometric Science of Information that was held at ENAC, Toulouse (France)

ISBN: 9783030654597$q(electronic bk.)

Standard No.: 10.1007/978-3-030-65459-7doiSubjects--Topical Terms:

198996
Manifolds (Mathematics)

LC Class. No.: QA613 / .P764 2021

Dewey Class. No.: 516.07

Progress in information geometrytheory and applications /
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505 0 $a Information Geometry of smooth densities on the Gaussian space: Poincare inequalities -- On Normalization Functions and ϕ-families of Probability Distributions -- Affine Connections with Torsion in (para-)complexified Structures -- Contact Hamiltonian systems for probability distribution functions and expectation variables: A study based on a class of master equations -- Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures -- Gauge freedom of entropies on q-Gaussian measures -- On geodesic triangles with right angles in a dually flat space -- Chain Rule Optimal Transport -- Towards the "Shape" of Cosmological Observables and the String Theory Landscape with Topological Data Analysis -- A review of two decades of correlations, hierarchies, networks and clustering in financial markets.
520 $a This 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 GSI'2019 - Geometric Science of Information that was held at ENAC, Toulouse (France)
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