Results 1 to 10 of about 248 (141)

Equivalence of Informations Characterizes Bregman Divergences [PDF]

Entropy
Bregman divergences form a class of distance-like comparison functions which plays fundamental roles in optimization, statistics, and information theory.
Philip S. Chodrow
exaly   +7 more sources

Symplectic Bregman Divergences [PDF]

Entropy
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality ...
Frank Nielsen
doaj   +5 more sources

Block-Active ADMM to Minimize NMF with Bregman Divergences [PDF]

Sensors, 2023
Over the last ten years, there has been a significant interest in employing nonnegative matrix factorization (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning.
Akhilesh Tyagi, Xinyao Li
exaly   +4 more sources

Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences [PDF]

Entropy, 2022
By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence.
Frank Nielsen
doaj   +2 more sources

Transport information Bregman divergences [PDF]

Information Geometry, 2021
Typos are ...
Wuchen Li, Wuchen Li
exaly   +4 more sources

On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds [PDF]

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
doaj   +2 more sources

Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity [PDF]

Entropy
Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning, among others. An exponential family can either be normalized subtractively by its cumulant or free energy function, or ...
Frank Nielsen
doaj   +2 more sources

On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid [PDF]

Entropy, 2020
The Jensen−Shannon divergence is a renown bounded symmetrization of the Kullback−Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar
Frank Nielsen
doaj   +2 more sources

Topological data analysis with Bregman divergences

Journal of Computational Geometry, 2019
We show that the framework of topological data analysis can be extended from metrics to Bregman divergences, widening the scope of possible applications. Examples are the Kullback-Leibler divergence, which is commonly used for comparing text and images,
Herbert Edelsbrunner, Hubert Wagner
doaj   +5 more sources

Matrix Nearness Problems with Bregman Divergences [PDF]

SIAM Journal on Matrix Analysis and Applications, 2008
This paper discusses a new class of matrix nearness problems that measure approximation error using a directed distance measure called a Bregman divergence. Bregman divergences offer an important generalization of the squared Frobenius norm and relative entropy, and they all share fundamental geometric properties.
Joel Tropp, Inderjit S Dhillon
exaly   +3 more sources