11,447 Results Found

Motivated by questions arising at the intersection of information theory and geometry, we compare two dissimilarity measures between finite categorical distributions. One is the well-known Jensen–Shannon divergence, which is easy to compute and...

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distributi...

The divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to...

In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a φ-function, the same function that is used in the definition of non-parametric φ-families. The pr...

The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the sc...

In the last years minimum phi-divergence estimators (MϕE) and phi-divergence test statistics (ϕTS) have been introduced as a very good alternative to classical likelihood ratio test and maximum likelihood estimator for different statistical problems....

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-clas...

This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable fr...

A recent canonical divergence, which is introduced on a smooth manifold ${\displaystyle \mathrm{M}}$ endowed with a general dualistic structure ${\displaystyle (\mathrm{g},\nabla ,{\nabla }^{*})}$ , is considered for flat ${\displaystyle \alpha }$ -connections. In the classical setting, we com...

When it is acknowledged that all candidate parameterised statistical models are misspecified relative to the data generating process, the decision maker (DM) must currently concern themselves with inference for the parameter value minimising the Kull...

The Kullback–Leibler (KL) divergence is a widely used measure for comparing probability distributions, but it faces limitations such as its unbounded nature and the lack of comparability between distributions with different quantum values (the...

Logarithmic score and information divergence appear in information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to regret functions and suc...

The relative entropy and the chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, the...

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...

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficu...

This paper investigates the potential of conceptual divergences within and between languages for providing intellectual resources for theorizing. Specifically, it explores the role of multilingual researchers in using the possibilities of the plurali...

We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associ...

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 non-uniform (skewed) mixture of probability density functions occurs in various disciplines. One needs a measure of similarity to the respective constituents and its bounds. We introduce a skewed Jensen–Fisher divergence based on relative Fisher in...

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...

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation, and the corresponding divergenc...

Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compres...

Generalisation error estimation is an important issue in machine learning. Cross-validation traditionally used for this purpose requires building multiple models and repeating the whole procedure many times in order to produce reliable error estimate...

This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of th...

The aim of this paper is to construct two new classes of multivariate risk statistics, and to study their properties. We, first, introduce the multivariate shortfall risk statistics and multivariate divergence risk statistics. Then, their basic prope...

The so-called controversy in elastohydrodynamic lubrication (EHL) regarding the nature of the shear dependence of viscosity, Eyring versus Carreau, is truly a controversy regarding the pressure and temperature dependence of low-shear viscosity. Roela...

This paper introduces a new family of the convex divergence-based risk measure by specifying $(h,\varphi )$ -divergence, corresponding with the dual representation. First, the sensitivity characteristics of the modified divergence risk measure with...

This study considers a new decomposition of an extended divergence on a foliation by deformed probability simplexes from the information geometry perspective. In particular, we treat the case where each deformed probability simplex corresponds to a s...

This article deals with new concepts in a product MV-algebra, namely, with the concepts of Rényi entropy and Rényi divergence. We define the Rényi entropy of order q of a partition in a product MV-algebra and its conditional vers...

A non-linear filtering algorithm based on the alpha-divergence is proposed, which uses the exponential family distribution to approximate the actual state distribution and the alpha-divergence to measure the approximation degree between the two distr...

Information geometry concerns the study of a dual structure ${\displaystyle (\mathrm{g},\nabla ,{\nabla }^{*})}$ upon a smooth manifold ${\displaystyle \mathrm{M}}$. Such a geometry is totally encoded within a potential function usually referred to as a divergence or contrast function of ${\displaystyle (\mathrm{g},\nabla ,{\nabla }^{*})}$...

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 states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.

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...

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...

Given finite-dimensional random vectors Y, X, and Z that form a Markov chain in that order ($Y\to X\to Z$), we derive the upper bounds on the excess minimum risk using generalized information divergence measures. Here, Y is a target vector to be es...

We introduce novel information-entropic variables—a Point Divergence Gain ( ${\mathsf{\Omega }}_{\alpha }^{(l\to m)}$ ), a Point Divergence Gain Entropy ( $I_{\alpha }$ ), and a Point Divergence Gain Entropy Density ( $P_{\alpha }$ )—which are derived from the Rényi entropy and...

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier–Stokes equation...

We examine the co-variability between the surface wind divergence and vorticity and how it varies with latitude in the Pacific Ocean using surface vector winds from reanalysis and satellite scatterometer observations. We show a strong correlation bet...

In this paper, we present a three-order, divergence-free finite volume scheme to simulate the steady state solar wind ambient. The divergence-free condition of the magnetic field is preserved by the constrained transport (CT) method. The CT method ca...

Owing to the lack of a unified ESG (environmental, social and governance) rating standard, notable inconsistencies have appeared in ESG ratings assigned to the same firm by various rating agencies. Based on data encompassing Chinese A-share listed co...

In recent years, corporate ESG performance has been widely incorporated into investment decisions and capital allocation considerations, becoming a focal point and hot topic for research by governments and organizations worldwide. However, due to var...

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R2 + such that the reconstruction wa...

Federated learning is a framework for multiple devices or institutions, called local clients, to collaboratively train a global model without sharing their data. For federated learning with a central server, an aggregation algorithm integrates model...

Air–sea fluxes are greatly enhanced by the winds and vertical exchanges generated by mesoscale convective systems (MCSs). In contrast to global numerical weather prediction models, space-borne scatterometers are able to resolve the small-scale...

Notothenioid fishes, a perciform group, radiated in the cold shelf waters around the Antarctic continent and the 110 species dominate fish diversity, abundance, and biomass at levels of ≈77%, 92%, and 91%, respectively. This occurred in a local...

The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutu...

Kullback–Leibler divergence $KL(p,q)$ is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computat...

This study investigates a laser ranging technology scheme featuring a large divergence angle for both the emitted and received laser beams, focusing on applications where both the measured target and the ranging carrier are high-mobility platforms. A...

We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leible...