Results 21 to 30 of about 7,890 (182)
Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity [PDF]
EntropyExponential 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 the Joint Convexity of the Bregman Divergence of Matrices [PDF]
Letters in Mathematical Physics, 2015 We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum Tsallis entropy of a tripartite state, which can be considered as a generalization of the strong subadditivity of the von Neumann entropy.
József Pitrik, Daniel Virosztek
exaly +4 more sources
Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center [PDF]
EntropyThe symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including ...
Frank Nielsen
doaj +2 more sources
Maximizing the Bregman divergence from a Bregman family [PDF]
Kybernetika, 2020 11 pages, 5 theorems, no ...
Johannes Rauh, Frantisek Matús
openaire +4 more sources
Comptes Rendus. Mécanique, 2023 With view on the context of convex thermomechanics, we propose tools based on the concept of Bregman divergence, a notion introduced in the 1960s and used in learning and optimization as well. This study is motivated by the need of “discrepancy measures”
Andrieux, Stéphane
doaj +1 more source
Hyperlink regression via Bregman divergence [PDF]
Neural Networks, 2020 41 pages, 14 ...
Akifumi Okuno, Hidetoshi Shimodaira
openaire +3 more sources
Transport information Bregman divergences [PDF]
Information Geometry, 2021 Typos are ...
openaire +3 more sources
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
doaj +1 more source
An Objective Prior from a Scoring Rule
Entropy, 2021 In this paper, we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in density ...
Stephen G. Walker, Cristiano Villa
doaj +1 more source
Minimax quantum state estimation under Bregman divergence [PDF]
Quantum, 2019 We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Koyama et al. [Entropy 19, 618 (2017)] for relative entropy, we find that given any estimator for a quantum state, there ...
Maria Quadeer +2 more
doaj +1 more source