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E-grāmata: Geometric Structures of Information

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Geometric Structures of InformationPalielināt
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This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing.





The book collects the most important contributions to the conference GSI2017 Geometric Science of Information.
Rho-Tau Embedding of Statistical Models
1(14)
Jan Naudts
Jun Zhang
A Class of Non-parametric Deformed Exponential Statistical Models
15(22)
Luigi Montrucchio
Giovanni Pistone
Statistical Manifolds Admitting Torsion and Partially Flat Spaces
37(14)
Masayuki Henmi
Hiroshi Matsuzoe
Conformal Flattening on the Probability Simplex and Its Applications to Voronoi Partitions and Centroids
51(18)
Atsumi Ohara
Monte Carlo Information-Geometric Structures
69(36)
Frank Nielsen
Gaetan Hadjeres
Information Geometry in Portfolio Theory
105(32)
Ting-Kam Leonard Wong
Generalising Frailty Assumptions in Survival Analysis: A Geometric Approach
137(12)
Vahed Maroufy
Paul Marriott
Some Universal Insights on Divergences for Statistics, Machine Learning and Artificial Intelligence
149(64)
Michel Broniatowski
Wolfgang Stummer
Information-Theoretic Matrix Inequalities and Diffusion Processes on Unimodular Lie Groups
213(38)
Gregory S. Chirikjian
Warped Rieman nian Metrics for Location-Scale Models
251(46)
Salem Said
Lionel Bombrun
Yannick Berthoumieu
Clustering in Hubert's Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices
297(36)
Frank Nielsen
Ke Sun
Jean-Louis Koszul and the Elementary Structures of Information Geometry
333
Frederic Barbaresco
Frank Nielsen is Professor at the Laboratoire d'informatique de l'École polytechnique, Paris, France. His research aims at understanding the nature and structure of information and randomness in data, and exploiting algorithmically this knowledge in innovative imaging applications. For that purpose, he coined the field of computational information geometry (computational differential geometry) to extract information as regular structures whilst taking into account variability in datasets by grounding them in geometric spaces. Geometry beyond Euclidean spaces has a long history of revolutionizing the way we perceived reality. Curved spacetime geometry, sustained relativity theory and fractal geometry unveiled the scale-free properties of Nature. In the digital world, geometry is data-driven and allows intrinsic data analytics by capturing the very essence of data through invariance principles without being biased by such or such particular data representation.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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