Results 1 to 10 of about 2,739 (95)

An Approach to Fisher-Rao Metric for Infinite Dimensional Non-Parametric Information Geometry [PDF]

Entropy
Non-parametric information geometry has long faced an “intractability barrier”: in the infinite-dimensional setting, the Fisher–Rao metric is a weak Riemannian metric functional that lacks a bounded inverse, rendering classical optimization and ...
Bing Cheng, Howell Tong
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Fisher–Rao Distance for Finite-Energy Signal Manifolds: Geometric Foundations and Numerical Analysis [PDF]

Entropy
This paper introduces a geometric framework for analyzing finite-energy signals observed with additive noise by representing them as points on statistical manifolds equipped with the Fisher–Rao metric. Each signal is associated with a parameter vector θ,
Franck Florin
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An Information-Geometric Justification for Composite Coherence in Event-Based Narrative Extraction [PDF]

Entropy
Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation.
Brian Keith-Norambuena
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Curve Registration of Functional Data for Approximate Bayesian Computation

Stats, 2021
Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures.
Anthony Ebert, Kerrie Mengersen, Fabrizio Ruggeri, Paul Wu   +3 more
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On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds

Entropy, 2020
We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat ...
Frank Nielsen
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The Fisher–Rao Distance between Multivariate Normal Distributions: Special Cases, Bounds and Applications

Entropy, 2020
The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms.
Julianna Pinele, João E. Strapasson, Sueli I. R. Costa   +2 more
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Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C^∗-Algebras

Entropy, 2020
A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework.
Florio M. Ciaglia, Jürgen Jost, Lorenz Schwachhöfer   +2 more
doaj   +1 more source

A Comparison between Wasserstein Distance and a Distance Induced by Fisher-Rao Metric in Complex Shapes Clustering

Proceedings, 2017
Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a human head in the space. The applications range from structural biology, computer vision, medical imaging to archaeology. We focus on the selection of an appropriate
Angela De Sanctis, Stefano A. Gattone
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Diffeological Statistical Models, the Fisher Metric and Probabilistic Mappings

Mathematics, 2020
We introduce the notion of a C k -diffeological statistical model, which allows us to apply the theory of diffeological spaces to (possibly singular) statistical models.
Hông Vân Lê
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Information-Theoretic Models for Physical Observables

Entropy, 2023
This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular ...
D. Bernal-Casas, J. M. Oller
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