A Lecture About the Use of Orlicz Spaces in Information Geometry

DOI10.1007/978-3-030-77957-3_10OpenAlexW3189060813MaRDI QIDQ5021899

Giovanni Pistone

Publication date: 14 January 2022

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.03376

Mathematics Subject Classification ID

Computer science (68-XX) Statistical mechanics, structure of matter (82-XX) Differential geometry (53-XX)

Cites Work

• 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
• Orlicz spaces and modular spaces
• Information geometry and its applications
• Some geometric calculations on Wasserstein space
• Functional analysis, Sobolev spaces and partial differential equations
• The exponential statistical manifold: mean parameters, orthogonality and space transformations
• Translations in the exponential Orlicz space with Gaussian weight
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Sobolev statistical manifolds and exponential models
• Information geometry of the Gaussian space
• Robust concentration inequalities in maximal exponential models
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Normal Approximations with Malliavin Calculus
• Computer Age Statistical Inference
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• Exponential models by Orlicz spaces and applications
• High-Dimensional Statistics
• High-Dimensional Probability
• Information Geometry of the Probability Simplex: A Short Course
• Information Geometry
• Nonparametric Information Geometry
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