Results 1 to 10 of about 62,953 (258)

On the Fisher Metric of Conditional Probability Polytopes [PDF]

Entropy, 2014
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of ...
Guido Montúfar, Johannes Rauh, Nihat Ay
doaj   +8 more sources

Geometry of Fisher Information Metric and the Barycenter Map [PDF]

Entropy, 2015
Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold \(X\).
Mitsuhiro Itoh, Hiroyasu Satoh
doaj   +4 more sources

Explicit Geodesic Projection Distance on the Statistical Manifold of Multivariate Elliptical Distributions [PDF]

Entropy
Geodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold.
Xiangbing Chen, Yingying Wang, Jihong Xiao   +2 more
doaj   +2 more sources

Weighted Relative Group Entropies and Associated Fisher Metrics

Entropy, 2022
A large family of new α-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may ...
Iulia-Elena Hirica, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae, Vasile Preda   +3 more
doaj   +3 more sources

The Fisher-Rao Metric for Projective Transformations of the Line [PDF]

International Journal of Computer Vision, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen J. Maybank
exaly   +4 more sources

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
doaj   +3 more sources

Approximation to the Fisher–Rao Metric for the Focus of Expansion [PDF]

Neurocomputing, 2008
The Fisher-Rao metric for the focus of expansion is approximated, under the assumption that the focus is estimated from correspondences between two images taken by a translating camera. The approximation is accurate if the errors in the image correspondences are small.
S J Maybank
exaly   +2 more sources

Fisher Vector Coding for Covariance Matrix Descriptors Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

Journal of Imaging, 2018
This paper presents an overview of coding methods used to encode a set of covariance matrices. Starting from a Gaussian mixture model (GMM) adapted to the Log-Euclidean (LE) or affine invariant Riemannian metric, we propose a Fisher Vector (FV ...
Ioana Ilea, Lionel Bombrun, Salem Said, Yannick Berthoumieu   +3 more
doaj   +3 more sources

Fractals via Controlled Fisher Iterated Function System

Fractal and Fractional, 2022
This paper explores the generalization of the fixed-point theorem for Fisher contraction on controlled metric space. The controlled metric space and Fisher contractions are playing a very crucial role in this research.
C. Thangaraj, D. Easwaramoorthy
doaj   +1 more source

Nonparametric Estimations and the Diffeological Fisher Metric [PDF]

, 2021
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending Lê's theory in \cite{Le2020} to include weakly $C^k$-diffeological statistical models.
Hông Vân Lê 0001, Alexey A. Tuzhilin
openaire   +3 more sources