Logarithmic divergences from optimal transport and Rényi geometry

DOI10.1007/s41884-018-0012-6zbMath1405.53039arXiv1712.03610OpenAlexW2962879179WikidataQ125364545 ScholiaQ125364545MaRDI QIDQ1713651

Ting-Kam Leonard Wong

Publication date: 28 January 2019

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

Full work available at URL: https://arxiv.org/abs/1712.03610

zbMATH Keywords

projective flatnessstatistical manifoldoptimal transportRényi divergence\(\alpha\)-divergencespaces of constant curvatureexponential concavity and convexity

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Characterization and structure theory of statistical distributions (62E10) Statistical aspects of information-theoretic topics (62B10) Local differential geometry (53B99) Linear and affine connections (53B05)

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Cites Work

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• The geometry of relative arbitrage
• Geometry of \(q\)-exponential family of probability distributions
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage
• From the Schrödinger problem to the Monge-Kantorovich problem
• Conjugate connections and Radon's theorem in affine differential geometry
• Optimization of relative arbitrage
• Information geometry and its applications
• Dual connections and affine geometry
• Second order efficiency of minimum contrast estimators in a curved exponential family
• Geometry of minimum contrast
• Geometry of contrast functions and conformal geometry
• On the divergence of 1-conformally flat statistical manifolds
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Unbalanced optimal transport: dynamic and Kantorovich formulations
• Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem
• Rho-tau embedding and gauge freedom in information geometry
• Embedding optimal transports in statistical manifolds
• Exponentially concave functions and a new information geometry
• Ricci curvature for parametric statistics via optimal transport
• Towards a canonical divergence within information geometry
• Multiplicative Schrödinger problem and the Dirichlet transport
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Inf-convolution, sous-additivite, convexite des fonctions numériques
• Rényi Divergence and Kullback-Leibler Divergence
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Variational Formulation of the Fokker--Planck Equation
• Divergence Function, Duality, and Convex Analysis
• Reference duality and representation duality in information geometry
• Geometric Modeling in Probability and Statistics
• Information Geometry
• Optimal Transport

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