Results 71 to 80 of about 248 (141)

Multidimensional Cost Geometry

Axioms
In this paper, we study the geometric structure induced by the canonical reciprocal cost function and its natural n-dimensional extension. In logarithmic coordinates, the potential depends only on the linear combination S=α·t, and the associated Hessian ...
Jonathan Washburn, Milan Zlatanović, Philip Beltracchi   +2 more
doaj   +1 more source

Fixed-Point Stability and Convergence of Deep Noncommutative Convolution Operators via Lyapunov-Divergence Operators

Boundary Value Problems
Fixed point theory is a rapidly developing area of mathematics that provides a unifying perspective across topology, optimization, and analysis. Classical theorems such as Brower’s, Banach’s contraction principle, Schauder’s topological theorems, and ...
Salah H. Alshabhi
doaj   +1 more source

On the Centroids of Symmetrized Bregman Divergences

CoRR, 2007
In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences are versatile, and unify quadratic geometric distances with various statistical entropic measures.
Frank Nielsen, Richard Nock
openaire   +2 more sources

Proper scoring rules and Bregman divergence

Bernoulli, 2018
We revisit the mathematical foundations of proper scoring rules (PSRs) and Bregman divergences and present their characteristic properties in a unified theoretical framework. In many situations it is preferable not to generate a PSR directly from its convex entropy on the unit simplex but instead by the sublinear extension of the entropy to the ...
openaire   +3 more sources

Bregman Divergences and Triangle Inequality [PDF]

Proceedings of the 2013 SIAM International Conference on Data Mining, 2013
Sreangsu Acharyya, Arindam Banerjee 0001, Daniel Boley   +2 more
openaire   +1 more source

Geometric Structures Induced by Deformations of the Legendre Transform. [PDF]

Entropy (Basel), 2023
Morales PA, Korbel J, Rosas FE.
europepmc   +1 more source

Revisiting Chernoff Information with Likelihood Ratio Exponential Families. [PDF]

Entropy (Basel), 2022
Nielsen F.
europepmc   +1 more source

A generalized Bayes framework for probabilistic clustering. [PDF]

Biometrika, 2023
Rigon T, Herring AH, Dunson DB.
europepmc   +1 more source

Conformal mirror descent with logarithmic divergences. [PDF]

Inf Geom, 2023
Kainth AS, Wong TL, Rudzicz F.
europepmc   +1 more source

A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions. [PDF]

Entropy (Basel), 2023
Nielsen F.
europepmc   +1 more source