Results 31 to 40 of about 326,200 (128)
, 2019 This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry.
openaire +4 more sources
Connecting Information Geometry and Geometric Mechanics
Entropy, 2017 The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q × Q .
Melvin Leok, Jun Zhang
doaj +1 more source
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
doaj +1 more source
Entropy, 2021 The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution ...
Masanari Kimura, Hideitsu Hino
doaj +1 more source
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
doaj +1 more source
Categorical Information Geometry
, 2023 Information geometry is the study of interactions between random variables by means of metric, divergences, and their geometry. Categorical probability has a similar aim, but uses algebraic structures, primarily monoidal categories, for that purpose.
openaire +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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.
openaire +5 more sources