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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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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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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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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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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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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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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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SMARANDACHE ANTI-GEOMETRY [PDF]
, 2004 This is an experimental geometry. All Hilbert's 20 axioms of the Euclidean GGeometry are denied in this vanguardist geometry of the real chaos: What is even more intriguing?
Bencze, Mihaly, Chimienti, Sandy P.
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