Results 41 to 50 of about 1,655,202 (268)
Kählerian Information Geometry for Signal Processing
Entropy, 2015 We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold.
Jaehyung Choi, Andrew P. Mullhaupt
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A Simple Approximation Method for the Fisher–Rao Distance between Multivariate Normal Distributions
Entropy, 2023 We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby normal ...
Frank Nielsen
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Geometric Structures Induced by Deformations of the Legendre Transform
Entropy, 2023 The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi’s divergence and entropy in a wide range of physical phenomena.
Pablo A. Morales +2 more
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Non-Metricity in Information Geometry
EntropyThe importance of non-metricity in information geometry is described through studies on gradient flow from the perspective of Weyl geometry. The Amari–Centsov tensor Ckij is the non-metricity tensor with respect to the α connection ∇(α) and Fisher metric
Tatsuaki Wada, Antonio Maria Scarfone
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Far from Asymptopia: Unbiased High-Dimensional Inference Cannot Assume Unlimited Data
Entropy, 2023 Inference from limited data requires a notion of measure on parameter space, which is most explicit in the Bayesian framework as a prior distribution. Jeffreys prior is the best-known uninformative choice, the invariant volume element from information ...
Michael C. Abbott, Benjamin B. Machta
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Geometry of Information Integration
, 2017 Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information ...
AB Barrett +16 more
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Change, time and information geometry
, 2000 Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time.
Caticha, Ariel
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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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Entropic Dynamics in a Theoretical Framework for Biosystems
Entropy, 2023 Central to an understanding of the physical nature of biosystems is an apprehension of their ability to control entropy dynamics in their environment.
Richard L. Summers
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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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