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TÃtulo : Geometric Science of Information : 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings / Tipo de documento: documento electrónico Autores: Nielsen, Frank, ; Barbaresco, Frédéric, Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2019 Número de páginas: XIX, 770 p. 317 ilustraciones, 53 ilustraciones en color. ISBN/ISSN/DL: 978-3-030-26980-7 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Inteligencia artificial MinerÃa de datos y descubrimiento de conocimientos Visión por computador Matemáticas de la Computación Matemáticas Informática Procesamiento de datos Clasificación: 40.151 Resumen: Este libro constituye las actas de la 4.ª Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2019, celebrada en Toulouse, Francia, en agosto de 2019. Los 79 artÃculos completos presentados en este volumen fueron cuidadosamente revisados ​​y seleccionados entre 105 presentaciones. Cubren todos los temas principales y destacados en el dominio de la ciencia geométrica de la información, incluidas las variedades de geometrÃa de la información de datos/información estructurados y sus aplicaciones avanzadas. Nota de contenido: Part I: Shape Space -- On geometric properties of the textile set and strict textile set -- Inexact elastic shape matching in the square root normal field framework -- Signatures in Shape Analysis: an Efficient Approach to Motion Identification -- Dilation operator approach for time/Doppler spectra characterization on SU(n) -- Selective metamorphosis for growth modelling with applications to landmarks -- Part II: Geometric Mechanics -- Intrinsic Incremental Mechanics -- -Multi-symplectic Extension of Lie Group Thermodynamics for Covariant Field Theories -- Euler-Poincare equation for Lie groups with non null symplectic cohomology. Application to the Mechanics -- Geometric numerical methods for mechanics -- Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups -- Part 3: Geometry of Tensor-Valued Data -- R-Complex Finsler Information Geometry Applied to Manifolds of Systems -- Minkowski Sum of Ellipsoids and Means of Covariance Matrices -- Hyperquaternions: An Efficient Mathematical Formalism for Geometry -- Alpha-power sums on symmetric cones -- Packing Bounds for Outer Products with Applications to Compressive Sensing -- Part 4: Lie Group Machine Learning -- On a method to construct exponential families by representation theory -- Lie Group Machine Learning & Gibbs Density on Poincare Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits -- Irreversible Langevin MCMC on Lie Groups -- Predicting Bending Moments with Machine Learning -- The exponential of nilpotent supergroups in the theory of Harish-Chandra representations -- Part 5: Geometric structures in thermodynamics and statistical physics -- Dirac structures in open thermodynamics -- From variational to single and double bracket formulations in nonequilibrium thermodynamics of simple systems -- A omological Approach to Belief Propagation and Bethe Approximations -- - About some systems-theoretic properties of Port Thermodynamic systems -- Expectation variables on a para-contact metric manifold exactly derived from master equations -- Part 6: Monotone embedding and affine immersion of probability models -- Doubly autoparallel structure and its applications -- Toeplitz Hermitian Positive Definite Matrix Machine Learning based on Fisher metric -- Deformed exponential and the behavior of the normalizing function -- Normalization problems for deformed exponential families -- New Geometry of parametric statistical Models -- Part 7: Divergence Geometry -- The Bregman chord divergence -- Testing the number and nature of components in a mixture distribution -- Robust etsimation by means of scaled Bregman power distances. Part I: Non-homogeneous data -- Robust estimation by means of scaled Bregman power distances. Part II: Extreme values -- Part 8: Computational Information Geometry -- Topological methods for unsupervised learning -- Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences -- The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models -- Parameter estimation with generalized empirical localization -- Properties of the cross entropy of ARMA processes -- Part 9: Statistical Manifold & Hessian Information Geometry -- Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature -- Inequalities for statistical submanifolds in sasakian statistical manifolds -- Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds -- Logarithmic divergence: geometry and interpretation of curvature -- Hessian Curvature and Optimal Transport -- Part 10: Non-parametric Information Geometry -- Divergence functions in Information Geometry -- Sobolev Statistical Manifolds and Exponential Models -- Minimization of the Kullback-Leibler divergence over a log-normal exponential arc -- Riemannian distance and diameter of the space of probability measures and the parametrix -- Part 11: Statistics on non-linear data -- A unified formulation for the Bures-Wassersteinand Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite operators -- Exploration of Balanced Metrics on Symmetric Positive Definite Matrices -- Affine-invariant midrange statistics -- Is affine-invariance well defined on SPD matrices? A principled continuum of metrics -- Shape part transfer via semantic latent space factorization -- Part 12: Geometric and structure preserving discretizations -- Variational discretization framework for geophysical flows -- Finite element methods for geometric evolution equations -- Local truncation error of low-order fractional variational integrators -- A partitioned finite element method for the structure-preserving discretization of damped in finite-dimensional port-Hamiltonian systems with boundary control -- Geometry, Energy, and Entropy Compatible (GEEC) variational approaches to various numerical schemes for fluid dynamics -- Part 13: Optimization on Manifold -- Canonical Moments for Optimal Uncertainty Quantification on a Variety -- Computational investigations of an obstacle-type shape optimization problem in the space of smooth shapes -- Bezier curves and C^2 interpolation in Riemannian Symmetric Spaces -- A Formalization of The Natural Gradient Method for General Similarity Measures -- The Frenet-Serret framework for aligning geometric curves -- Part 14: Geometry of Quantum States -- When geometry meets psycho-physics and quantum mechanics: Modern perspectives on the space of perceived colors -- Quantum statistical manifolds: The finite-dimensional case -- Generalized Gibbs Ensembles in Discrete Quantum Gravity -- On the notion of composite system, classical and quantum -- Part 15: Probability on Riemannian Manifolds -- The Riemannian barycentre as a proxy for global optimization -- Hamiltonian Monte Carlo on Lie groups and constrained mechanics on homogeneous manifolds -- On the Fisher Rao information metric in the space of normal distributions -- Simulation of Conditioned Diffusions on the Flat Torus -- Towards parametric bi-invariant density estimation on SE(2) -- Part 16: Wasserstein Information Geometry / Optimal Transport -- Affine Natural Proximal Learning -- Parametric Fokker-Planck equation -- Multi-marginal Schroedinger bridges -- Hopf-Cole transformation and Schrodinger problems -- - Curvature of the manifold of fixed-rank positive-semidefinite matrices endowed with the Bures-Wasserstein metric -- Part 17: Geometric Science of Information Libraries -- Second-order networks in PyTorch -- Symmetric Algorithmic Components for Shape Analysis with Dieomorphisms. Tipo de medio : Computadora Summary : This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Geometric Science of Information : 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings / [documento electrónico] / Nielsen, Frank, ; Barbaresco, Frédéric, . - 1 ed. . - [s.l.] : Springer, 2019 . - XIX, 770 p. 317 ilustraciones, 53 ilustraciones en color.
ISBN : 978-3-030-26980-7
Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos.
Idioma : Inglés (eng)
Palabras clave: Inteligencia artificial MinerÃa de datos y descubrimiento de conocimientos Visión por computador Matemáticas de la Computación Matemáticas Informática Procesamiento de datos Clasificación: 40.151 Resumen: Este libro constituye las actas de la 4.ª Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2019, celebrada en Toulouse, Francia, en agosto de 2019. Los 79 artÃculos completos presentados en este volumen fueron cuidadosamente revisados ​​y seleccionados entre 105 presentaciones. Cubren todos los temas principales y destacados en el dominio de la ciencia geométrica de la información, incluidas las variedades de geometrÃa de la información de datos/información estructurados y sus aplicaciones avanzadas. Nota de contenido: Part I: Shape Space -- On geometric properties of the textile set and strict textile set -- Inexact elastic shape matching in the square root normal field framework -- Signatures in Shape Analysis: an Efficient Approach to Motion Identification -- Dilation operator approach for time/Doppler spectra characterization on SU(n) -- Selective metamorphosis for growth modelling with applications to landmarks -- Part II: Geometric Mechanics -- Intrinsic Incremental Mechanics -- -Multi-symplectic Extension of Lie Group Thermodynamics for Covariant Field Theories -- Euler-Poincare equation for Lie groups with non null symplectic cohomology. Application to the Mechanics -- Geometric numerical methods for mechanics -- Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups -- Part 3: Geometry of Tensor-Valued Data -- R-Complex Finsler Information Geometry Applied to Manifolds of Systems -- Minkowski Sum of Ellipsoids and Means of Covariance Matrices -- Hyperquaternions: An Efficient Mathematical Formalism for Geometry -- Alpha-power sums on symmetric cones -- Packing Bounds for Outer Products with Applications to Compressive Sensing -- Part 4: Lie Group Machine Learning -- On a method to construct exponential families by representation theory -- Lie Group Machine Learning & Gibbs Density on Poincare Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits -- Irreversible Langevin MCMC on Lie Groups -- Predicting Bending Moments with Machine Learning -- The exponential of nilpotent supergroups in the theory of Harish-Chandra representations -- Part 5: Geometric structures in thermodynamics and statistical physics -- Dirac structures in open thermodynamics -- From variational to single and double bracket formulations in nonequilibrium thermodynamics of simple systems -- A omological Approach to Belief Propagation and Bethe Approximations -- - About some systems-theoretic properties of Port Thermodynamic systems -- Expectation variables on a para-contact metric manifold exactly derived from master equations -- Part 6: Monotone embedding and affine immersion of probability models -- Doubly autoparallel structure and its applications -- Toeplitz Hermitian Positive Definite Matrix Machine Learning based on Fisher metric -- Deformed exponential and the behavior of the normalizing function -- Normalization problems for deformed exponential families -- New Geometry of parametric statistical Models -- Part 7: Divergence Geometry -- The Bregman chord divergence -- Testing the number and nature of components in a mixture distribution -- Robust etsimation by means of scaled Bregman power distances. Part I: Non-homogeneous data -- Robust estimation by means of scaled Bregman power distances. Part II: Extreme values -- Part 8: Computational Information Geometry -- Topological methods for unsupervised learning -- Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences -- The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models -- Parameter estimation with generalized empirical localization -- Properties of the cross entropy of ARMA processes -- Part 9: Statistical Manifold & Hessian Information Geometry -- Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature -- Inequalities for statistical submanifolds in sasakian statistical manifolds -- Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds -- Logarithmic divergence: geometry and interpretation of curvature -- Hessian Curvature and Optimal Transport -- Part 10: Non-parametric Information Geometry -- Divergence functions in Information Geometry -- Sobolev Statistical Manifolds and Exponential Models -- Minimization of the Kullback-Leibler divergence over a log-normal exponential arc -- Riemannian distance and diameter of the space of probability measures and the parametrix -- Part 11: Statistics on non-linear data -- A unified formulation for the Bures-Wassersteinand Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite operators -- Exploration of Balanced Metrics on Symmetric Positive Definite Matrices -- Affine-invariant midrange statistics -- Is affine-invariance well defined on SPD matrices? A principled continuum of metrics -- Shape part transfer via semantic latent space factorization -- Part 12: Geometric and structure preserving discretizations -- Variational discretization framework for geophysical flows -- Finite element methods for geometric evolution equations -- Local truncation error of low-order fractional variational integrators -- A partitioned finite element method for the structure-preserving discretization of damped in finite-dimensional port-Hamiltonian systems with boundary control -- Geometry, Energy, and Entropy Compatible (GEEC) variational approaches to various numerical schemes for fluid dynamics -- Part 13: Optimization on Manifold -- Canonical Moments for Optimal Uncertainty Quantification on a Variety -- Computational investigations of an obstacle-type shape optimization problem in the space of smooth shapes -- Bezier curves and C^2 interpolation in Riemannian Symmetric Spaces -- A Formalization of The Natural Gradient Method for General Similarity Measures -- The Frenet-Serret framework for aligning geometric curves -- Part 14: Geometry of Quantum States -- When geometry meets psycho-physics and quantum mechanics: Modern perspectives on the space of perceived colors -- Quantum statistical manifolds: The finite-dimensional case -- Generalized Gibbs Ensembles in Discrete Quantum Gravity -- On the notion of composite system, classical and quantum -- Part 15: Probability on Riemannian Manifolds -- The Riemannian barycentre as a proxy for global optimization -- Hamiltonian Monte Carlo on Lie groups and constrained mechanics on homogeneous manifolds -- On the Fisher Rao information metric in the space of normal distributions -- Simulation of Conditioned Diffusions on the Flat Torus -- Towards parametric bi-invariant density estimation on SE(2) -- Part 16: Wasserstein Information Geometry / Optimal Transport -- Affine Natural Proximal Learning -- Parametric Fokker-Planck equation -- Multi-marginal Schroedinger bridges -- Hopf-Cole transformation and Schrodinger problems -- - Curvature of the manifold of fixed-rank positive-semidefinite matrices endowed with the Bures-Wasserstein metric -- Part 17: Geometric Science of Information Libraries -- Second-order networks in PyTorch -- Symmetric Algorithmic Components for Shape Analysis with Dieomorphisms. Tipo de medio : Computadora Summary : This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...]
TÃtulo : Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings / Tipo de documento: documento electrónico Autores: Nielsen, Frank, ; Barbaresco, Frédéric, Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2021 Número de páginas: XXIX, 929 p. 179 ilustraciones, 102 ilustraciones en color. ISBN/ISSN/DL: 978-3-030-80209-7 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Visión por computador Matemáticas de la Computación IngenierÃa Informática y Redes Matemáticas Inteligencia artificial Red informática Informática IngenierÃa Informática Clasificación: 40.151 Resumen: Este libro constituye las actas de la Quinta Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2021, celebrada en ParÃs, Francia, en julio de 2021. Los 98 artÃculos presentados en este volumen fueron cuidadosamente revisados ​​y seleccionados entre 125 presentaciones. Cubren todos los temas principales y destacados en el dominio de la ciencia geométrica de la información, incluidas las variedades de geometrÃa de la información de datos/información estructurados y sus aplicaciones avanzadas. Los artÃculos están organizados en los siguientes temas: Probabilidad y estadÃstica de variedades de Riemann; geometrÃa subriemanniana y neuromatemática; da forma a los espacios; geometrÃa de estados cuánticos; discretizaciones geométricas y que preservan la estructura; geometrÃa de la información en fÃsica; Mentira aprendizaje automático grupal; métodos geométricos y simplécticos para modelos hidrodinámicos; análisis armónico de grupos de Lie; variedad estadÃstica y geometrÃa de la información de Hesse; mecánica geométrica; entropÃa deformada, entropÃa cruzada y entropÃa relativa; geometrÃa de la información de transformación; estadÃstica, información y topologÃa; aprendizaje profundo geométrico; estructuras topológicas y geométricas en neurociencias; geometrÃa de la información computacional; colector y optimización; estadÃsticas de divergencia; transporte y aprendizaje óptimos; y estructuras geométricas en termodinámica y fÃsica estadÃstica. Nota de contenido: Probability and Statistics on Riemannian Manifolds -- From Bayesian inference to MCMC and convex optimisation in Hadamard manifolds -- Finite Sample Smeariness on Spheres -- Gaussian distributions on Riemannian symmetric spaces in the large N limit -- Smeariness Begets Finite Sample Smeariness -- Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces -- Quinten Tupker, Salem Said and Cyrus MostajeranSub-Riemannian Geometry and Neuromathematics -- Submanifolds of fixed degree in graded manifolds for perceptual completion -- An auditory cortex model for sound processing -- Conformal model of hypercolumns in V1 cortex and the Moebius group. Application to the visual stability problem -- Extremal controls for Duits car -- Multi-Shape Registration with Constrained Deformations -- Shapes Spaces -- Geodesics of the Quotient-Affine Metrics on Full-Rank Correlation Matrices -- Parallel Transport on Kendall Shape Spaces -- Diffusion Means and Heat Kernel on Manifolds -- A reduced parallel transport equation on Lie Groups with a left-invariant metric -- Currents and K-functions for Fiber Point Processes -- Geometry of Quantum States -- Q-Information Geometry of Systems -- Group actions and Monotone Metric Tensors: The qubit case -- Quantum Jensen-Shannon divergences between infinite-dimensional positive definite operators -- Towards a geometrization of quantum complexity and chaos -- Hunt's colorimetric effect from a quantum measurement viewpoint -- Geometric and Structure Preserving Discretizations -- The Herglotz principle and vakonomic dynamics -- Structure-preserving discretization of a coupled heat-wave system, as interconnected port-Hamiltonian systems -- Examples of symbolic and numerical computation in Poisson geometry.-New directions for contact integrators -- Information Geometry in Physics -- Space-time thermo-mechanics for a material continuum -- Entropic dynamics yields reciprocal relations -- Lie Group Machine Learning.-Gibbs states on symplectic manifolds with symmetries -- Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau's Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map -- On Gaussian Group Convex Models -- Exponential-wrapped probability densities on SL(2,C) -- Information Geometry and Hamiltonian Systems on Lie Groups -- Geometric and Symplectic Methods for Hydrodynamical Models -- Multisymplectic variational integrators for fluid models with constraints -- Metriplectic Integrators for Dissipative Fluids -- From quantum hydrodynamics to Koopman wavefunctions I -- From quantum hydrodynamics to Koopman wavefunctions II -- Harmonic Analysis on Lie Groups -- The Fisher information of curved exponential families and the elegant Kagan inequality -- Continuous Wavelet transforms for vector-valued functions -- Entropy under disintegrations -- Koszul Information Geometry, Liouville-Mineur Integrable Systems and Moser Isospectral Deformation Method for Hermitian Positive-Definite Matrices -- Flapping Wing Coupled Dynamics in Lie Group Setting -- Statistical Manifold and Hessian Information Geometry -- Canonical foliations of statistical manifolds with hyperbolic compact leaves -- Open problems in global analysis. Structured foliations and the information Geometry -- Curvature inequalities and Simons' type formulas in statistical geometry -- Harmonicity of Conformally-Projectively Equivalent Statistical Manifolds and Conformal Statistical Submersions -- Algorithms for approximating means of semi-infinite quasi-Toeplitz matrices -- Geometric Mechanics -- Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation -- Bridge Simulation and Metric Estimation on Lie Groups -- Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition -- Non-relativistic Limits of General Relativity -- Deformed Entropy,Cross-entropy, and Relative Entropy -- A Primer on Alpha-Information Theory with Application to Leakage in Secrecy Systems -- Schrödinger encounters Fisher and Rao: a survey -- Projections with logarithmic divergences -- Chernoff, Bhattacharyya, Rényi andSharma-Mittal divergence analysis for Gaussian stationary ARMA processes -- Transport Information Geometry -- Wasserstein statistics in one-dimensional location-scale models -- Traditional and accelerated gradient descent for neural architecture search -- Recent developments on the MTW tensor -- Wasserstein Proximal of GANs -- Statistics, Information and Topology -- Information cohomology of classical vector-valued observables -- On Marginal Estimation Algorithms - Belief Propagation as Diffusion -- Towards a functorial description of quantum relative entropy -- Frobenius Statistical manifolds & geometric invariants -- Geometric Deep Learning -- SU(1, 1) Equivariant Neural Networks and Application to Robust Toeplitz HermitianPositive Definite Matrix Classification -- Iterative SE(3)-Transformers -- End-to-End Similarity Learning and Hierarchical clustering for unfixed size datasets -- Information theory and the embedding problem for Riemannian manifolds -- cCorrGAN: Conditional CorrGAN for Learning Empirical Conditional Distributions in the Correlation Elliptope -- Topological and Geometrical Structures in Neurosciences -- Topological Model of Neural Information Networks -- On Information Links -- Betti Curves of Rank One Symmetric Matrices -- Algebraic Homotopy Interleaving Distance -- A Python hands-on tutorial on network and topological neuroscience -- Computational Information Geometry -- Computing statistical divergences with sigma points -- Remarks to Laplacian of graphical models in various graphs -- Classification in the Siegel space for vectorial autoregressive data -- Information Metrics for Phylogenetic Trees via Distributions of Discrete and Continuous Characters -- Wald Space for Phylogenetic Trees -- Necessary Condition for Semiparametric Efficiency of Experimental Designs -- Parametrisation Independence of the Natural Gradient in Overparametrised Systems -- Properties of nonlinear diffusion equations on networks and their geometric aspects -- Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian -- Statistical bundle of the transport model -- Manifolds and Optimization -- Endpoint Quasi-geodesics on the Stiefel Manifold -- Optimization of a shape metric based on information theory applied to segmentation fusion and evaluation in multimodal MRI for DIPG tumor analysis -- Metamorphic image registration using a semi-Lagrangian scheme -- Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric -- Divergence Statistics -- On f-divergences between Cauchy distributions -- Transport information Hessian distances -- Minimization with respect to divergences and applications -- Optimal transport with some directed distances -- Robust Empirical Likelihood -- Optimal Transport and Learning -- Mind2Mind : Transfer Learning for GANs -- Fast and asymptotic steering to a steady state for networks flows -- Geometry of Outdoor Virus Avoidance in Cities -- A Particle-Evolving method for approximating the Optimal Transport plan -- Geometric Structures in Thermodynamics and Statistical Physics -- Schrödinger problem for lattice gases: a heuristic point of view -- A variational perspective on the thermodynamics of non-isothermal reacting open systems -- On the Thermodynamic Interpretation of Deep Learning Systems -- Dirac structures in thermodynamics of non-simple systems. Tipo de medio : Computadora Summary : This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings / [documento electrónico] / Nielsen, Frank, ; Barbaresco, Frédéric, . - 1 ed. . - [s.l.] : Springer, 2021 . - XXIX, 929 p. 179 ilustraciones, 102 ilustraciones en color.
ISBN : 978-3-030-80209-7
Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos.
Idioma : Inglés (eng)
Palabras clave: Visión por computador Matemáticas de la Computación IngenierÃa Informática y Redes Matemáticas Inteligencia artificial Red informática Informática IngenierÃa Informática Clasificación: 40.151 Resumen: Este libro constituye las actas de la Quinta Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2021, celebrada en ParÃs, Francia, en julio de 2021. Los 98 artÃculos presentados en este volumen fueron cuidadosamente revisados ​​y seleccionados entre 125 presentaciones. Cubren todos los temas principales y destacados en el dominio de la ciencia geométrica de la información, incluidas las variedades de geometrÃa de la información de datos/información estructurados y sus aplicaciones avanzadas. Los artÃculos están organizados en los siguientes temas: Probabilidad y estadÃstica de variedades de Riemann; geometrÃa subriemanniana y neuromatemática; da forma a los espacios; geometrÃa de estados cuánticos; discretizaciones geométricas y que preservan la estructura; geometrÃa de la información en fÃsica; Mentira aprendizaje automático grupal; métodos geométricos y simplécticos para modelos hidrodinámicos; análisis armónico de grupos de Lie; variedad estadÃstica y geometrÃa de la información de Hesse; mecánica geométrica; entropÃa deformada, entropÃa cruzada y entropÃa relativa; geometrÃa de la información de transformación; estadÃstica, información y topologÃa; aprendizaje profundo geométrico; estructuras topológicas y geométricas en neurociencias; geometrÃa de la información computacional; colector y optimización; estadÃsticas de divergencia; transporte y aprendizaje óptimos; y estructuras geométricas en termodinámica y fÃsica estadÃstica. Nota de contenido: Probability and Statistics on Riemannian Manifolds -- From Bayesian inference to MCMC and convex optimisation in Hadamard manifolds -- Finite Sample Smeariness on Spheres -- Gaussian distributions on Riemannian symmetric spaces in the large N limit -- Smeariness Begets Finite Sample Smeariness -- Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces -- Quinten Tupker, Salem Said and Cyrus MostajeranSub-Riemannian Geometry and Neuromathematics -- Submanifolds of fixed degree in graded manifolds for perceptual completion -- An auditory cortex model for sound processing -- Conformal model of hypercolumns in V1 cortex and the Moebius group. Application to the visual stability problem -- Extremal controls for Duits car -- Multi-Shape Registration with Constrained Deformations -- Shapes Spaces -- Geodesics of the Quotient-Affine Metrics on Full-Rank Correlation Matrices -- Parallel Transport on Kendall Shape Spaces -- Diffusion Means and Heat Kernel on Manifolds -- A reduced parallel transport equation on Lie Groups with a left-invariant metric -- Currents and K-functions for Fiber Point Processes -- Geometry of Quantum States -- Q-Information Geometry of Systems -- Group actions and Monotone Metric Tensors: The qubit case -- Quantum Jensen-Shannon divergences between infinite-dimensional positive definite operators -- Towards a geometrization of quantum complexity and chaos -- Hunt's colorimetric effect from a quantum measurement viewpoint -- Geometric and Structure Preserving Discretizations -- The Herglotz principle and vakonomic dynamics -- Structure-preserving discretization of a coupled heat-wave system, as interconnected port-Hamiltonian systems -- Examples of symbolic and numerical computation in Poisson geometry.-New directions for contact integrators -- Information Geometry in Physics -- Space-time thermo-mechanics for a material continuum -- Entropic dynamics yields reciprocal relations -- Lie Group Machine Learning.-Gibbs states on symplectic manifolds with symmetries -- Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau's Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map -- On Gaussian Group Convex Models -- Exponential-wrapped probability densities on SL(2,C) -- Information Geometry and Hamiltonian Systems on Lie Groups -- Geometric and Symplectic Methods for Hydrodynamical Models -- Multisymplectic variational integrators for fluid models with constraints -- Metriplectic Integrators for Dissipative Fluids -- From quantum hydrodynamics to Koopman wavefunctions I -- From quantum hydrodynamics to Koopman wavefunctions II -- Harmonic Analysis on Lie Groups -- The Fisher information of curved exponential families and the elegant Kagan inequality -- Continuous Wavelet transforms for vector-valued functions -- Entropy under disintegrations -- Koszul Information Geometry, Liouville-Mineur Integrable Systems and Moser Isospectral Deformation Method for Hermitian Positive-Definite Matrices -- Flapping Wing Coupled Dynamics in Lie Group Setting -- Statistical Manifold and Hessian Information Geometry -- Canonical foliations of statistical manifolds with hyperbolic compact leaves -- Open problems in global analysis. Structured foliations and the information Geometry -- Curvature inequalities and Simons' type formulas in statistical geometry -- Harmonicity of Conformally-Projectively Equivalent Statistical Manifolds and Conformal Statistical Submersions -- Algorithms for approximating means of semi-infinite quasi-Toeplitz matrices -- Geometric Mechanics -- Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation -- Bridge Simulation and Metric Estimation on Lie Groups -- Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition -- Non-relativistic Limits of General Relativity -- Deformed Entropy,Cross-entropy, and Relative Entropy -- A Primer on Alpha-Information Theory with Application to Leakage in Secrecy Systems -- Schrödinger encounters Fisher and Rao: a survey -- Projections with logarithmic divergences -- Chernoff, Bhattacharyya, Rényi andSharma-Mittal divergence analysis for Gaussian stationary ARMA processes -- Transport Information Geometry -- Wasserstein statistics in one-dimensional location-scale models -- Traditional and accelerated gradient descent for neural architecture search -- Recent developments on the MTW tensor -- Wasserstein Proximal of GANs -- Statistics, Information and Topology -- Information cohomology of classical vector-valued observables -- On Marginal Estimation Algorithms - Belief Propagation as Diffusion -- Towards a functorial description of quantum relative entropy -- Frobenius Statistical manifolds & geometric invariants -- Geometric Deep Learning -- SU(1, 1) Equivariant Neural Networks and Application to Robust Toeplitz HermitianPositive Definite Matrix Classification -- Iterative SE(3)-Transformers -- End-to-End Similarity Learning and Hierarchical clustering for unfixed size datasets -- Information theory and the embedding problem for Riemannian manifolds -- cCorrGAN: Conditional CorrGAN for Learning Empirical Conditional Distributions in the Correlation Elliptope -- Topological and Geometrical Structures in Neurosciences -- Topological Model of Neural Information Networks -- On Information Links -- Betti Curves of Rank One Symmetric Matrices -- Algebraic Homotopy Interleaving Distance -- A Python hands-on tutorial on network and topological neuroscience -- Computational Information Geometry -- Computing statistical divergences with sigma points -- Remarks to Laplacian of graphical models in various graphs -- Classification in the Siegel space for vectorial autoregressive data -- Information Metrics for Phylogenetic Trees via Distributions of Discrete and Continuous Characters -- Wald Space for Phylogenetic Trees -- Necessary Condition for Semiparametric Efficiency of Experimental Designs -- Parametrisation Independence of the Natural Gradient in Overparametrised Systems -- Properties of nonlinear diffusion equations on networks and their geometric aspects -- Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian -- Statistical bundle of the transport model -- Manifolds and Optimization -- Endpoint Quasi-geodesics on the Stiefel Manifold -- Optimization of a shape metric based on information theory applied to segmentation fusion and evaluation in multimodal MRI for DIPG tumor analysis -- Metamorphic image registration using a semi-Lagrangian scheme -- Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric -- Divergence Statistics -- On f-divergences between Cauchy distributions -- Transport information Hessian distances -- Minimization with respect to divergences and applications -- Optimal transport with some directed distances -- Robust Empirical Likelihood -- Optimal Transport and Learning -- Mind2Mind : Transfer Learning for GANs -- Fast and asymptotic steering to a steady state for networks flows -- Geometry of Outdoor Virus Avoidance in Cities -- A Particle-Evolving method for approximating the Optimal Transport plan -- Geometric Structures in Thermodynamics and Statistical Physics -- Schrödinger problem for lattice gases: a heuristic point of view -- A variational perspective on the thermodynamics of non-isothermal reacting open systems -- On the Thermodynamic Interpretation of Deep Learning Systems -- Dirac structures in thermodynamics of non-simple systems. Tipo de medio : Computadora Summary : This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...]
TÃtulo : Geometric Science of Information : Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings Tipo de documento: documento electrónico Autores: Nielsen, Frank, ; Barbaresco, Frédéric, Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2017 Número de páginas: XXV, 877 p. 168 ilustraciones ISBN/ISSN/DL: 978-3-319-68445-1 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Visión por computador Inteligencia artificial Informática Protección de datos Matemáticas de la Computación Seguridad de datos e información Clasificación: 006.37 Resumen: Este libro constituye las actas arbitradas de la Tercera Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2017, celebrada en ParÃs, Francia, en noviembre de 2017. Los 101 artÃculos completos presentados fueron cuidadosamente revisados ​​y seleccionados entre 113 presentaciones y están organizados en los siguientes temas : estadÃsticas sobre datos no lineales; espacio de forma; transporte óptimo y aplicaciones: procesamiento de imágenes; transporte óptimo y aplicaciones: procesamiento de señales; variedad estadÃstica y geometrÃa de información de arpillera; incrustación monótona en geometrÃa de información; estructura de la información en neurociencia; robótica geométrica y seguimiento; mecánica geométrica y robótica; mecánica geométrica estocástica y termodinámica de grupos de Lie; probabilidad en variedades de Riemann; geometrÃa de divergencia; geometrÃa de información no paramétrica; optimización en colector; geometrÃa de la información computacional; estimación de densidad de probabilidad; geometrÃa de sesión de datos con valores tensoriales; métodos geodésicos con restricciones; Aplicaciones de la geometrÃa a distancia. Nota de contenido: Statistics on non-linear data -- Shape space -- Optimal Transport & Applications -- Statistical Manifold & Hessian Information Geometry -- Statistical Manifold and Hessian Information Geometry -- Monotone Embedding in Information Geometry -- Information Structure in Neuroscience -- Geometric Robotics and Tracking -- Geometric Mechanics and Robotics -- Stochastic Geometric Mechanics and Lie Group Thermodynamics -- Probability on Riemannian Manifolds -- Divergence Geometry -- Non-parametric Information Geometry -- Optimization on Manifold -- Computational Information Geometry -- Probability Density Estimation -- Session Geometry of Tensor-Valued Data -- Geodesic Methods with Constraints -- Applications of Distance Geometry. Tipo de medio : Computadora Summary : This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Geometric Science of Information : Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings [documento electrónico] / Nielsen, Frank, ; Barbaresco, Frédéric, . - 1 ed. . - [s.l.] : Springer, 2017 . - XXV, 877 p. 168 ilustraciones.
ISBN : 978-3-319-68445-1
Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos.
Idioma : Inglés (eng)
Palabras clave: Visión por computador Inteligencia artificial Informática Protección de datos Matemáticas de la Computación Seguridad de datos e información Clasificación: 006.37 Resumen: Este libro constituye las actas arbitradas de la Tercera Conferencia Internacional sobre Ciencias Geométricas de la Información, GSI 2017, celebrada en ParÃs, Francia, en noviembre de 2017. Los 101 artÃculos completos presentados fueron cuidadosamente revisados ​​y seleccionados entre 113 presentaciones y están organizados en los siguientes temas : estadÃsticas sobre datos no lineales; espacio de forma; transporte óptimo y aplicaciones: procesamiento de imágenes; transporte óptimo y aplicaciones: procesamiento de señales; variedad estadÃstica y geometrÃa de información de arpillera; incrustación monótona en geometrÃa de información; estructura de la información en neurociencia; robótica geométrica y seguimiento; mecánica geométrica y robótica; mecánica geométrica estocástica y termodinámica de grupos de Lie; probabilidad en variedades de Riemann; geometrÃa de divergencia; geometrÃa de información no paramétrica; optimización en colector; geometrÃa de la información computacional; estimación de densidad de probabilidad; geometrÃa de sesión de datos con valores tensoriales; métodos geodésicos con restricciones; Aplicaciones de la geometrÃa a distancia. Nota de contenido: Statistics on non-linear data -- Shape space -- Optimal Transport & Applications -- Statistical Manifold & Hessian Information Geometry -- Statistical Manifold and Hessian Information Geometry -- Monotone Embedding in Information Geometry -- Information Structure in Neuroscience -- Geometric Robotics and Tracking -- Geometric Mechanics and Robotics -- Stochastic Geometric Mechanics and Lie Group Thermodynamics -- Probability on Riemannian Manifolds -- Divergence Geometry -- Non-parametric Information Geometry -- Optimization on Manifold -- Computational Information Geometry -- Probability Density Estimation -- Session Geometry of Tensor-Valued Data -- Geodesic Methods with Constraints -- Applications of Distance Geometry. Tipo de medio : Computadora Summary : This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Geometric Structures of Statistical Physics, Information Geometry, and Learning / Barbaresco, Frédéric ; Nielsen, Frank
TÃtulo : Geometric Structures of Statistical Physics, Information Geometry, and Learning : SPIGL'20, Les Houches, France, July 27–31 / Tipo de documento: documento electrónico Autores: Barbaresco, Frédéric, ; Nielsen, Frank, Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2021 Número de páginas: XIII, 459 p. 87 ilustraciones, 63 ilustraciones en color. ISBN/ISSN/DL: 978-3-030-77957-3 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: TeorÃa y métodos estadÃsticos. Informática Matemáticas Inteligencia artificial FÃsica EstadÃstica EstadÃstica Aplicaciones matemáticas en informática Clasificación: 004.0151 Resumen: El aprendizaje automático y la inteligencia artificial utilizan cada vez más herramientas metodológicas basadas en la fÃsica estadÃstica. Por el contrario, las limitaciones y dificultades encontradas en la IA cuestionan los fundamentos mismos de la fÃsica estadÃstica. Esta interacción entre la IA y la fÃsica estadÃstica ha sido atestiguada desde el nacimiento de la IA, y los principios que sustentan la fÃsica estadÃstica pueden arrojar nueva luz sobre la base conceptual de la IA. Durante los últimos cincuenta años, la fÃsica estadÃstica ha sido investigada a través de nuevas estructuras geométricas que permiten la formalización covariante de la termodinámica. Los métodos de inferencia en el aprendizaje automático han comenzado a adaptar estas nuevas estructuras geométricas para procesar datos en espacios de representación más abstractos. Este volumen recopila contribuciones seleccionadas sobre la interacción de la fÃsica estadÃstica y la inteligencia artificial. El objetivo es proporcionar un diálogo constructivo en torno a una base común que permita el establecimiento de nuevos principios y leyes que regulen estas dos disciplinas de manera unificada. Las contribuciones se presentaron en el taller sobre Estructuras conjuntas y fundamento común de la fÃsica estadÃstica, la geometrÃa de la información y la inferencia para el aprendizaje que se celebró en Les Houches en julio de 2020. Los diversos enfoques teóricos se discuten en el contexto de sus posibles aplicaciones en los sistemas cognitivos. aprendizaje automático, procesamiento de señales. Nota de contenido: PART 1: Tribute to Jean-Marie Souriau seminal works: G. de Saxcé and C.-M. Marle, Structure des Systèmes Dynamiques -- Jean-Marie Souriau's book 50th birthday -- F. Barbaresco, Jean-Marie Souriau's Symplectic Model of Statistical Physics : Seminal papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum -- PART 2: Lie Group Geometry & Diffeological Model of Statistical Physics and Information Geometry: F. Barbaresco - Souriau-Casimir Lie Groups Thermodynamics & Machine Learning -- K. Tojo and T. Yoshino, An exponential family on the upper half plane and its conjugate prior -- E. Chevallier and N. Guigui, Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces -- G. de Saxcé, Galilean Thermodynamics of Continua -- H. Vân Lê and A. Tuzhilin, Nonparametric estimations and the diffeological Fisher metric -- PART 3: Advanced Geometrical Models of Statistical Manifolds in Information Geometry: J.-P. Francoise, Information Geometry and Integrable Hamiltonian Systems -- M. N. Boyom, Relevant Differential topology in statistical manifolds -- G. Pistone, A lecture about the use of Orlicz Spaces in Information Geometry -- F. Nielsen and G. Hadjeres, Quasiconvex Jensen divergences and quasiconvex Bregman divergences -- PART 4: Geometric Structures of Mechanics, Thermodynamics & Inference for Learning: F. Gay-Balmaz and H. Yoshimura, Dirac Structures and Variational Formulation of Thermodynamics for Open Systems -- A. A. Simoes, D. MartÃn de Diego, M. L. Valcázar and Manuel de León, The geometry of some thermodynamic systems -- F. Chinesta, E. Cueto, M. Grmela, B. Mioya, M. Pavelka and M. Sipka, Learning Physics from Data: a Thermodynamic Interpretation -- Z. Terze, V. Pandža, M. Andrić and D. Zlatar, Computational dynamics of reduced coupled multibody-fluid system in Lie group setting -- F. Masi, I. Stefanou, P. Vannucci and V. Maffi-Berthier, Material modeling via Thermodynamics-based Artificial Neural Networks -- K. Grosvenor, Information Geometry and Quantum Fields -- PART 5: Hamiltonian Monte Carlo, HMC Sampling and Learning on Manifolds: A. Barp, The Geometric Integration of Measure-Preserving Flows for Sampling and Hamiltonian Monte Carlo -- A. Fradi, I. Adouani and C. Samir, Bayesian inference on local distributions of functions and multidimensional curves with spherical HMC sampling -- S. Huntsman, Sampling and Statistical Physics via Symmetry -- T. Gerald, H. Zaatiti and H. Hajri, A Practical hands-on for learning Graph Data Communities on Manifolds. Tipo de medio : Computadora Summary : Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Geometric Structures of Statistical Physics, Information Geometry, and Learning : SPIGL'20, Les Houches, France, July 27–31 / [documento electrónico] / Barbaresco, Frédéric, ; Nielsen, Frank, . - 1 ed. . - [s.l.] : Springer, 2021 . - XIII, 459 p. 87 ilustraciones, 63 ilustraciones en color.
ISBN : 978-3-030-77957-3
Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos.
Idioma : Inglés (eng)
Palabras clave: TeorÃa y métodos estadÃsticos. Informática Matemáticas Inteligencia artificial FÃsica EstadÃstica EstadÃstica Aplicaciones matemáticas en informática Clasificación: 004.0151 Resumen: El aprendizaje automático y la inteligencia artificial utilizan cada vez más herramientas metodológicas basadas en la fÃsica estadÃstica. Por el contrario, las limitaciones y dificultades encontradas en la IA cuestionan los fundamentos mismos de la fÃsica estadÃstica. Esta interacción entre la IA y la fÃsica estadÃstica ha sido atestiguada desde el nacimiento de la IA, y los principios que sustentan la fÃsica estadÃstica pueden arrojar nueva luz sobre la base conceptual de la IA. Durante los últimos cincuenta años, la fÃsica estadÃstica ha sido investigada a través de nuevas estructuras geométricas que permiten la formalización covariante de la termodinámica. Los métodos de inferencia en el aprendizaje automático han comenzado a adaptar estas nuevas estructuras geométricas para procesar datos en espacios de representación más abstractos. Este volumen recopila contribuciones seleccionadas sobre la interacción de la fÃsica estadÃstica y la inteligencia artificial. El objetivo es proporcionar un diálogo constructivo en torno a una base común que permita el establecimiento de nuevos principios y leyes que regulen estas dos disciplinas de manera unificada. Las contribuciones se presentaron en el taller sobre Estructuras conjuntas y fundamento común de la fÃsica estadÃstica, la geometrÃa de la información y la inferencia para el aprendizaje que se celebró en Les Houches en julio de 2020. Los diversos enfoques teóricos se discuten en el contexto de sus posibles aplicaciones en los sistemas cognitivos. aprendizaje automático, procesamiento de señales. Nota de contenido: PART 1: Tribute to Jean-Marie Souriau seminal works: G. de Saxcé and C.-M. Marle, Structure des Systèmes Dynamiques -- Jean-Marie Souriau's book 50th birthday -- F. Barbaresco, Jean-Marie Souriau's Symplectic Model of Statistical Physics : Seminal papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum -- PART 2: Lie Group Geometry & Diffeological Model of Statistical Physics and Information Geometry: F. Barbaresco - Souriau-Casimir Lie Groups Thermodynamics & Machine Learning -- K. Tojo and T. Yoshino, An exponential family on the upper half plane and its conjugate prior -- E. Chevallier and N. Guigui, Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces -- G. de Saxcé, Galilean Thermodynamics of Continua -- H. Vân Lê and A. Tuzhilin, Nonparametric estimations and the diffeological Fisher metric -- PART 3: Advanced Geometrical Models of Statistical Manifolds in Information Geometry: J.-P. Francoise, Information Geometry and Integrable Hamiltonian Systems -- M. N. Boyom, Relevant Differential topology in statistical manifolds -- G. Pistone, A lecture about the use of Orlicz Spaces in Information Geometry -- F. Nielsen and G. Hadjeres, Quasiconvex Jensen divergences and quasiconvex Bregman divergences -- PART 4: Geometric Structures of Mechanics, Thermodynamics & Inference for Learning: F. Gay-Balmaz and H. Yoshimura, Dirac Structures and Variational Formulation of Thermodynamics for Open Systems -- A. A. Simoes, D. MartÃn de Diego, M. L. Valcázar and Manuel de León, The geometry of some thermodynamic systems -- F. Chinesta, E. Cueto, M. Grmela, B. Mioya, M. Pavelka and M. Sipka, Learning Physics from Data: a Thermodynamic Interpretation -- Z. Terze, V. Pandža, M. Andrić and D. Zlatar, Computational dynamics of reduced coupled multibody-fluid system in Lie group setting -- F. Masi, I. Stefanou, P. Vannucci and V. Maffi-Berthier, Material modeling via Thermodynamics-based Artificial Neural Networks -- K. Grosvenor, Information Geometry and Quantum Fields -- PART 5: Hamiltonian Monte Carlo, HMC Sampling and Learning on Manifolds: A. Barp, The Geometric Integration of Measure-Preserving Flows for Sampling and Hamiltonian Monte Carlo -- A. Fradi, I. Adouani and C. Samir, Bayesian inference on local distributions of functions and multidimensional curves with spherical HMC sampling -- S. Huntsman, Sampling and Statistical Physics via Symmetry -- T. Gerald, H. Zaatiti and H. Hajri, A Practical hands-on for learning Graph Data Communities on Manifolds. Tipo de medio : Computadora Summary : Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...]
