Results 11 to 20 of about 245,725 (186)

On Minimum Bregman Divergence Inference

Mathematics
The density power divergence (DPD) is a well-studied member of the Bregman divergence family and forms the basis of widely used minimum divergence estimators that balance efficiency and robustness. In this paper, we introduce and study a new sub-class of
Soumik Purkayastha, Ayanendranath Basu
doaj   +4 more sources

Preconditioner Design via the Bregman Divergence [PDF]

CoRR, 2023
We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence.
Bock, Andreas, Andersen, Martin S.
core   +4 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   +8 more sources

Bregman–Hausdorff Divergence: Strengthening the Connections Between Computational Geometry and Machine Learning

Machine Learning and Knowledge Extraction
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures.
Tuyen Pham, Hana Dal Poz Kouřimská, Hubert Wagner   +2 more
doaj   +2 more sources

Understanding Higher-Order Interactions in Information Space [PDF]

Entropy
Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an
Herbert Edelsbrunner, Katharina Ölsböck, Hubert Wagner   +2 more
doaj   +2 more sources

Revisiting Chernoff Information with Likelihood Ratio Exponential Families [PDF]

Entropy, 2022
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance.
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

Information Geometry and Asymptotic Theory for SMML Estimators [PDF]

Entropy
Strict minimum message length (SMML) is an information-theoretic coding principle that represents a continuous statistical model by a finite set of assertions and a partition of the sample space.
Enes Makalic, Daniel F. Schmidt
doaj   +2 more sources

Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center [PDF]

Entropy
The 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

Bregman-divergence-based Arimoto-Blahut algorithm [PDF]

IEEE Transactions on Information Theory
We generalize the generalized Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. In existing methods, when linear constraints are imposed, each iteration needs to solve a convex minimization.
Hayashi, Masahito
core   +6 more sources