Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space

DOI10.1007/s41884-022-00078-6arXiv2210.07641OpenAlexW4309890093MaRDI QIDQ6138791

Giovanni Pistone

Publication date: 16 January 2024

Published in: Information Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.07641

zbMATH Keywords

information geometryexponential manifoldstatistical bundleGaussian Orlicz-Sobolev spacedually flat affine manifold

Mathematics Subject Classification ID

Statistics (62-XX) Communication, information (94Axx) Sufficiency and information (62Bxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computational Optimal Transport: With Applications to Data Science
• Examples of the application of nonparametric information geometry to statistical physics
• New results on mixture and exponential models by Orlicz spaces
• Information geometry formalism for the spatially homogeneous Boltzmann equation
• Proper local scoring rules
• Orlicz spaces and modular spaces
• Exponential statistical manifold
• Information geometry and its applications
• Some geometric calculations on Wasserstein space
• Functional analysis, Sobolev spaces and partial differential equations
• The geometry of exponential families
• Defining the curvature of a statistical problem (with applications to second order efficiency)
• Wasserstein Riemannian geometry of Gaussian densities
• Natural gradient via optimal transport
• Differential geometry of curved exponential families. Curvatures and information loss
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Statistical bundle of the transport model
• Kantorovich distance on finite metric spaces: Arens-Eells norm and CUT norms
• Information geometry of the Gaussian space
• Robust concentration inequalities in maximal exponential models
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Uniqueness of the Fisher–Rao metric on the space of smooth densities
• Normal Approximations with Malliavin Calculus
• Computer Age Statistical Inference
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• High-Dimensional Statistics
• High-Dimensional Probability
• Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities
• Information Geometry
• Nonparametric Information Geometry

This page was built for publication: Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space