Results 31 to 40 of about 1,655,202 (268)
Transversely Hessian foliations and information geometry [PDF]
, 2015 A family of probability distributions parametrized by an open domain $\Lambda$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite.
Boyom, Michel Nguiffo, Wolak, Robert A.
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The Information Geometry of UMAP
Le Matematiche, 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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On Monotone Embedding in Information Geometry
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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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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How Morphological Computation Shapes Integrated Information in Embodied Agents
Frontiers in Psychology, 2021 The Integrated Information Theory provides a quantitative approach to consciousness and can be applied to neural networks. An embodied agent controlled by such a network influences and is being influenced by its environment.
Carlotta Langer +5 more
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, 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.
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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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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
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Information geometry, dynamics and discrete quantum mechanics [PDF]
, 2013 We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture.
Hall, Michael J. W., Reginatto, Marcel
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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.
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