Results 21 to 30 of about 407,884 (290)
Information Geometry of Nonlinear Stochastic Systems [PDF]
Entropy, 2018 We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and ...
Rainer Hollerbach +2 more
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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.
Perrone, Paolo
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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
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An Information Geometry-Based Track-Before-Detect Algorithm for Range-Azimuth Measurements in Radar Systems. [PDF]
Entropy (Basel)The detection of weak moving targets in heterogeneous clutter backgrounds is a significant challenge in radar systems. In this paper, we propose a track-before-detect (TBD) method based on information geometry (IG) theory applied to range-azimuth ...
Liu J, Wu H, Yang Z, Hua X, Cheng Y.
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, 2017 The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.
Lê, Hông Vân +7 more
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On Monotone Embedding in Information Geometry [PDF]
Entropy, 2015 A paper was published (Harsha and Subrahamanian Moosath, 2014) in which the authors claimed to have discovered an extension to Amari's \(\alpha\)-geometry through a general monotone embedding function. It will be pointed out here that this so-called \((F,
Jun Zhang
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Information Geometry for the Working Information Theorist
CoRR, 2023 Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient ...
Kumar, M. Ashok +2 more
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The Information Geometry of UMAP
CoRR, 2023 12 pages, 2 figures, 3 tables ; Github repo (https://github.com/sashakolpakov/info-geometry-umap) ; to appear in Le ...
Alexander Kolpakov \ University of Neuch\^atel, Switzerland +2 more
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Syntax and Geometry of Information
Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2023 This paper presents an information-theoretical model of syntactic generalization. We study syntactic generalization from the perspective of the capacity to disentangle semantic and structural information, emulating the human capacity to assign a grammaticality judgment to semantically nonsensical sentences. In order to isolate the structure, we propose
Bailly, Raphaël +2 more
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Biology, geometry and information [PDF]
Theory in Biosciences, 2021 AbstractThe main thesis developed in this article is that the key feature of biological life is the a biological process can control and regulate other processes, and it maintains that ability over time. This control can happen hierarchically and/or reciprocally, and it takes place in three-dimensional space.
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