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Geometry of information: Classical and quantum aspects [PDF]
Theoretical Computer Science, 2022 In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic enrichments.
Noemie Combe +2 more
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On preferred point geometry in statistics [PDF]
, 2001 A brief synopsis of progress in differential geometry in statistics is followed by a note of some points of tension in the developing relationship between these disciplines. The preferred point nature of much of statistics is described and suggests the
Marriott, P. +9 more
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Computational Information Geometry in Statistics: Theory and Practice
Entropy, 2014 A broad view of the nature and potential of computational information geometry in statistics is offered. This new area suitably extends the manifold-based approach of classical information geometry to a simplicial setting, in order to obtain an ...
Frank Critchley, Paul Marriott
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Information geometry of the spherical model [PDF]
Physical Review E, 2003 Motivated by previous observations that geometrizing statistical mechanics offers an interesting alternative to more standard approaches,we have recently calculated the curvature (the fundamental object in this approach) of the information geometry metric for the Ising model on an ensemble of planar random graphs.
Janke, W., Johnston, D. A., Kenna, R.
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The basics of information geometry [PDF]
AIP Conference Proceedings, 2015 To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".
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Information geometry and the renormalization group [PDF]
Physical Review E, 2015 1 + 20 Pages, LaTeX. References added, Discussions improved. Version accepted in Phys.
Maity, Reevu +2 more
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Global Solvably Closed Anabelian Geometry [PDF]
, 2006 In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have ...
Mochizuki, Shinichi
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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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On Perfect Obfuscation: Local Information Geometry Analysis [PDF]
, 2020 We consider the problem of privacy-preserving data release for a specific utility task under perfect obfuscation constraint. We establish the necessary and sufficient condition to extract features of the original data that carry as much information about
Behrooz Razeghi +11 more
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