Results 51 to 60 of about 59,568 (301)
Foundations of Structural Statistics: Statistical Manifolds
CoRR, 2020 Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices, which in the category of statistical models are induced by statistical divergences.
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Conformal Control Tools for Statistical Manifolds and for γ-Manifolds
Mathematics, 2022 The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ-manifolds are introduced. New conformal invariant tools are defined. A necessary condition for the f-conformal equivalence of γ-manifolds is found, extending that for the α-conformal equivalence for statistical manifolds ...
Iulia-Elena Hirica +3 more
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Statistical manifold with degenerate metric
, 2023 A statistical manifold is a pseudo-Riemannian manifold endowed with a Codazzi structure. This structure plays an important role in Information Geometry and its related fields, e.g., a statistical model admits this structure with the Fisher-Rao metric.
Kayo, Kaito
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Latent Network Construction for Univariate Time Series Based on Variational Auto-Encode
Entropy, 2021 Time series analysis has been an important branch of information processing, and the conversion of time series into complex networks provides a new means to understand and analyze time series.
Jiancheng Sun +4 more
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Entropy, 2015 In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending ...
Alina-Daniela Vîlcu +1 more
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F-Geometry and Amari’s α-Geometry on a Statistical Manifold
Entropy, 2014 In this paper, we introduce a geometry called F-geometry on a statistical manifold S using an embedding F of S into the space RX of random variables. Amari’s α-geometry is a special case of F-geometry.
Harsha K. V. +1 more
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Characterizations of Transversal Lightlike Submanifolds in Indefinite Golden Statistical Geometry
MathematicsWe investigate transversal and radical transversal lightlike submanifolds (TLSs) of indefinite golden statistical manifolds (IGSMs). Using the dual affine connections associated with statistical structures, we obtain decomposition formulas and derive ...
Md Aquib
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Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds
Mathematics, 2019 Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R ×
Aliya Naaz Siddiqui +2 more
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Statistical connections on decomposable Riemann manifold
, 2020 Let (M, g, phi) be an n-dimensional locally decomposable Riemann manifold, that is, g(phi X, Y) = g(X, phi Y) and del phi = 0, where del is Riemann (Levi-Civita) connection of metric g. In this paper, we construct a new connection on locally decomposable
KARAMAN, Çağrı
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Hypersurfaces in statistical manifolds
Differential Geometry and its Applications, 2009 A statistical structure on a manifold \(M\) consists of a Riemannian metric \(g\) and a torsion-free affine connection \(\nabla\) that satisfies \( (\nabla_Xg)(Y,Z) = (\nabla_Yg)(X,Z)\) for all vector fields \(X\), \(Y\), and \(Z\) on \(M\). The statistical manifold \((M, \nabla, g)\) has constant curvature \(k\) if \[ R^\nabla(X,Y)Z = k(g(Y,Z)X-g(X,Z ...
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