Related papers: On Weighted Extropies
We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…
The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more…
Loop-weighted walk with parameter $\lambda\geq 0$ is a non-Markovian model of random walks that is related to the loop $O(N)$ model of statistical mechanics. A walk receives weight $\lambda^{k}$ if it contains $k$ loops; whether this is a…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…
In this paper, we introduce the weighted cumulative residual Mathai--Haubold entropy and establish its fundamental properties. A dynamic version is developed, and its behavior under linear transformations is studied. Bounds and explicit…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
In statistical analysis, quantifying uncertainties through measures such as entropy, extropy, varentropy, and varextropy is of fundamental importance for understanding distribution functions. This paper investigates several properties of…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
We introduce novel information-entropic variables -- a Point Divergence Gain (${\Omega}^{(l \rightarrow m)}_\alpha$), a Point Divergence Gain Entropy ($I_\alpha$), and a Point Divergence Gain Entropy Density ($P_\alpha$) -- which are…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
We propose using the technique of weighted citation to measure an article's prestige. The technique allocates a different weight to each reference by taking into account the impact of citing journals and citation time intervals. Weighted…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We consider the quantum resource theory of measurement informativeness and introduce a weight-based quantifier of informativeness. We show that this quantifier has operational significance from the perspective of quantum state exclusion, by…
The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while…