Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric,...
This paper introduces a new family of the convex divergence-based risk measure by specifying ( h , ϕ ) -divergence, corresponding with the dual representation. First, the sensitivity characteristics of the modified divergence risk measure with...
The article deals with the definitions of the distance, divergence, and similarity characteristics between two finite fuzzy measures, which are generalizations of the same definitions between two finite probability distributions. As is known, a fuzzy...
Statistical predictive analysis is a very useful tool for predicting future observations. Previous literature has addressed both Bayesian and non-Bayesian predictive distributions of future statistics based on past sufficient statistics. This study f...
The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms pro...
In the literature of information theory and fuzzy set doctrine, there exist various prominent measures of divergence; each possesses its own merits, demerits, and disciplines of applications. Divergence measure is a tool to compute the discrimination...
Despite advancements in divergence and distance measures across fuzzy set extensions, the development of such measures for Globular T-Spherical Fuzzy Sets (G-TSFSs) remains significantly unexplored. Existing approaches often fall short in capturing t...
The present Special Issue of Entropy, entitled Information and Divergence Measures, covers various aspects and applications in the general area of Information and Divergence Measures [...]
In statistical inference, the information-theoretic performance limits can often be expressed in terms of a statistical divergence between the underlying statistical models (e.g., in binary hypothesis testing, the error probability is related to the...
A divergence measure plays a crucial part in discriminating two probability distributions and drawing inferences constructed on such discrimination. The intention of this study is to propose such a divergence measure based on Jensen inequality and ex...
Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-...
This paper presents an analysis of different despeckling filters applied on both synthetically corrupted optical images and actual Synthetic Aperture Radar (SAR) images. Several authors use optical images as ground truth and then the images are corru...
An in-plane radial sensitivity interferometer that uses the divergent illumination for displacement measurement in the radial direction is presented. A description and mathematical model for calculating the sensitivity vector are also presented. The...
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based on generali...
Fuzzy set theory has extensively employed various divergence measure methods to quantify distinctions between two elements. The primary objective of this study is to introduce a generalized divergence measure integrated into the Technique for Order o...
The approach for estimating and testing based on divergence measures has become, in the last 30 years, a very popular technique not only in the field of statistics, but also in other areas, such as machine learning, pattern recognition, etc [...]
Iterative reconstruction of density pixel images from measured projections in computed tomography has attracted considerable attention. The ordered-subsets algorithm is an acceleration scheme that uses subsets of projections in a previously decided o...
In the last decades the interest in statistical methods based on information measures and particularly in pseudodistances or divergences has grown substantially [...]
Given finite-dimensional random vectors Y, X, and Z that form a Markov chain in that order (Y→X→Z), we derive the upper bounds on the excess minimum risk using generalized information divergence measures. Here, Y is a target vector to be es...
In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic func...
Chronic obstructive pulmonary disease (COPD) is the third leading cause of death worldwide. Pulmonary function tests (PFTs) and quantitative indices (QIs) of computed tomography (CT) are typically used to diagnose COPD. The purpose of this work was t...
Changes in food consumption, physical inactivity, and other lifestyle habits are potential causes of the obesity epidemic. Paradoxically, the media promotes idealization of a leaner body appearance. Under these circumstances, self-perception of weigh...
This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties. We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergences...
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bay...
In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this pap...
Classification of the divergence measure for fuzzy sets (FSs) has been a successful approach since it has been utilized in several disciplines, e.g., image segmentation, pattern recognition, decision making, etc. The objective of the manuscript is to...
In the presented article, we define the R-norm entropy and the conditional R-norm entropy of partitions of a given fuzzy probability space and study the properties of the suggested entropy measures. In addition, we introduce the concept of R-norm div...
In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional...
The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symm...
In this study, we introduce and rigorously formalize the notion of (P, m)-superquadratic stochastic processes, representing a novel and far-reaching generalization of classical convex stochastic processes. By exploring their intrinsic structural char...
Information theory can be used to analyze the cost–benefit of visualization processes. However, the current measure of benefit contains an unbounded term that is neither easy to estimate nor intuitive to interpret. In this work, we propose to r...
Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measur...
In this paper, we present a radial basis function (RBF) and cubature Kalman filter (CKF) based enhanced fusion strategy for vision and inertial integrated attitude measurement for sampling frequency discrepancy and divergence. First, the multi-freque...
We introduce fractal Tsallis entropy and show that it satisfies Shannon–Khinchin axioms. Analogously to Tsallis divergence (or Tsallis relative entropy, according to some authors), fractal Tsallis divergence is defined and some properties of it are s...
In this paper, we propose a method for optimizing the parameter values in iterative reconstruction algorithms that include adjustable parameters in order to optimize the reconstruction performance. Specifically, we focus on the power divergence-based...
Many visual representations, such as volume-rendered images and metro maps, feature a noticeable amount of information loss due to a variety of many-to-one mappings. At a glance, there seem to be numerous opportunities for viewers to misinterpret the...
In this paper, we present a general framework that provides a comprehensive and uniform treatment of integral majorization inequalities for convex functions and finite signed measures. Along with new results, we present unified and simple proofs of c...
Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restr...
Two families of dependence measures between random variables are introduced. They are based on the Rényi divergence of order α and the relative...
In the Bayesian framework, the usual choice of prior in the prediction of homogeneous Poisson processes with random effects is the gamma one. Here, we propose the use of higher order maximum entropy priors. Their advantage is illustrated in a simulat...
Predicting electricity prices and demand is a very important issue for the energy market industry. In order to improve the accuracy of any predictive model, a previous variable importance analysis is highly advised. In this paper, we propose an alter...
A fully adaptive particle filtering algorithm is proposed in this paper which is capable of updating both state process models and measurement models separately and simultaneously. The approach is a significant step toward more realistic online monit...
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symm...
Information content and compression are tightly related concepts that can be addressed through both classical and algorithmic information theories, on the basis of Shannon entropy and Kolmogorov complexity, respectively. The definition of several ent...
Specific emitter identification (SEI) techniques are often used in civilian and military spectrum-management operations, and they are also applied to support the security and authentication of wireless communication. In this letter, a new SEI method...
We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownia...
Data science, information theory, probability theory, statistical learning, statistical signal processing, and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures [...]
The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of t...
Testing of evidence in criminal cases can be limited by temporal or financial constraints or by the fact that certain tests may be mutually exclusive, so choosing the tests that will have maximal impact on the final result is essential. In this paper...
In this paper, we suggest an approach to recovering behavior-related, preference-choice network information from observational data. We model the process as a self-organized behavior based random exponential network-graph system. To address the unkno...
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