Results 41 to 50 of about 1,328,298 (163)
Lifting Dual Connections with the Riemann Extension
Mathematics, 2020 Let (M,g) be a Riemannian manifold equipped with a pair of dual connections (∇,∇*). Such a structure is known as a statistical manifold since it was defined in the context of information geometry.
Stéphane Puechmorel
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Lie groupoids in information geometry
, 2019 We demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one provided by Lie groupoids and Lie algebroids.
Amari S-I +11 more
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F‐Manifolds and geometry of information [PDF]
Bulletin of the London Mathematical Society, 2020 The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since 1990's. The focus of this paper consists in the demonstration that various spaces of
Combe , N., Manin, Y.
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On the Fisher Metric of Conditional Probability Polytopes
Entropy, 2014 We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of ...
Guido Montúfar, Johannes Rauh, Nihat Ay
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Interest rates and information geometry [PDF]
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001 20 pages, 3 ...
Brody, D C, Hughston, L P
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Entropy, 2017 Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds ...
Yongqiang Cheng, Xuezhi Wang, Bill Moran
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Hamilton-Jacobi Theory and Information Geometry
, 2017 Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been ...
C Lanczos +17 more
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Entropy, 2018 This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices ...
Xiaoqiang Hua +3 more
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AxiomsA critical processing step for AI algorithms is mapping the raw data to a landscape where the similarity of two data points is conveniently defined. Frequently, when the data points are compositions of probability functions, the similarity is reduced to ...
Giovanni Pistone, Muhammad Shoaib
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Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
Entropy, 2021 Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems.
Eun-jin Kim
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