The Jeffreys divergence is a renown arithmetic symmetrization of the oriented Kullback–Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various tec...
In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generaliz...
We investigate the asymptotic properties of the plug-in estimator for the Jeffreys divergence, the symmetric variant of the Kullback–Leibler (KL) divergence. This study focuses specifically on the divergence between discrete distributions. Trad...
In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are p...
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weig...
This paper aims at certain theoretical studies and additional computational analysis on symmetry and its lack in Kullback-Leibler and Jeffreys probabilistic divergences related to some engineering applications. As it is known, the Kullback-Leibler di...
The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multiva...
The geometric Jensen–Shannon divergence (G-JSD) has gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the...
This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior retur...
This paper presents the entropic damage indicators for metallic material fatigue processes obtained from three associated energy dissipation sources. Since its inception, reliability engineering has employed statistical and probabilistic models to as...
Home advantage in sports is important for coaches, players, fans, and commentators and has a key role in sports prediction models. This paper builds on results of recent research that—instead of points gained—used goals scored and goals c...
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 Jensen–Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback–Leibler divergence which measures the total Kullback–Leibler divergence to the average mixture distribution. However, the Jensen–Shan...
The ability of participants to monitor the correctness of their own decisions by rating their confidence is a form of metacognition. This introspective act is crucial for many aspects of cognition, including perception, memory, learning, emotion regu...
The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The update reproduces the new observations and interpolates using prior information. The optimal update is obtained by m...
Clustering sets of histograms has become popular thanks to the success of the generic method of bag-of-X used in text categorization and in visual categorization applications. In this paper, we investigate the use of a parametric family of distortion...
A measurement performed on a quantum system is an act of gaining information about its state. However, in the foundations of quantum theory, the concept of information is multiply defined, particularly in the area of quantum reconstruction, and its c...
Bayesian testing of a point null hypothesis is considered. The null hypothesisis that an observation, x, is distributed according to the normal distribution with a mean ofzero and known variance q2. The alternative hypothesis is that x is distributed...
In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing p...
In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of stron...
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...
In this study, we consider the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. In...
Population genetics describes evolutionary processes, focusing on the variation within and between species and the forces shaping this diversity. Evolution reflects information accumulated in genomes, enhancing organisms’ adaptation to their en...
One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this pa...
We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby nor...
Wireless capsule endoscopy (WCE) has great advantages over traditional endoscopy because it is portable and easy to use, especially in remote monitoring health-services. However, during the WCE process, the large amount of captured video data demands...
Living systems can be understood as organized entities that capture, transform, and reproduce information. Classical gene-centered models explain adaptation through frequency changes driven by differential fitness, yet they often overlook the higher-...
There is a large amount of remote sensing data available for land use and land cover (LULC) classification and thus optimizing selection of remote sensing variables is a great challenge. Although many methods such as Jeffreys–Matusita (JM) distance a...