Results 11 to 20 of about 500 (159)

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   +3 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

Anomaly Detection in High-Dimensional Time Series Data with Scaled Bregman Divergence [PDF]

Algorithms
The purpose of anomaly detection is to identify special data points or patterns that significantly deviate from the expected or typical behavior of the majority of the data, and it has a wide range of applications across various domains.
Yunge Wang, Lingling Zhang, Tong Si, Graham Bishop, Haijun Gong   +4 more
doaj   +2 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.
Xinyao Li, Akhilesh Tyagi
doaj   +2 more sources

A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model

Entropy, 2017
In image and signal processing, the beta-divergence is well known as a similarity measure between two positive objects. However, it is unclear whether or not the distance-like structure of beta-divergence is preserved, if we extend the domain of the beta-
Hyenkyun Woo
exaly   +3 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

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.
Daniel Virosztek, József Pitrik
exaly   +4 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