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.
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 Souriaus 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.
Lisainfo e-raamatute kohta