Nonparametric Information Geometry

DOI10.1007/978-3-642-40020-9_3zbMath1311.94023arXiv1306.0480OpenAlexW1596429603MaRDI QIDQ5410510

Giovanni Pistone

Publication date: 16 April 2014

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0480

zbMATH Keywords

information geometryBanach manifold

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Information theory (general) (94A15)

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Information geometry formalism for the spatially homogeneous Boltzmann equation ⋮ Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space ⋮ Legendre duality: from thermodynamics to information geometry ⋮ Lagrangian and Hamiltonian dynamics for probabilities on the statistical bundle ⋮ Metric on the space of quantum states from relative entropy. Tomographic reconstruction ⋮ Unnamed Item ⋮ Wasserstein Riemannian geometry of Gaussian densities ⋮ Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities ⋮ A Class of Non-parametric Deformed Exponential Statistical Models ⋮ A Lecture About the Use of Orlicz Spaces in Information Geometry ⋮ Rényi relative entropy from homogeneous Kullback-Leibler divergence Lagrangian

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