Related papers: Weighted information and entropy rates
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
Weighted Updating generalizes Bayesian updating, allowing for biased beliefs by weighting the likelihood function and prior distribution with positive real exponents. I provide a rigorous foundation for the model by showing that…
In this work, we propose two information generating functions: general weighted information and relative information generating functions, and study their properties. { It is shown that the general weighted information generating function…
In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a…
The extropy is a measure of information introduced by Lad et al. (2015) as dual to entropy. As the entropy, it is a shift-independent information measure. We introduce here the notion of weighted extropy, a shift-dependent information…
The notion of weighted quantum entropy is reviewed and considered for bipartite and noncomposite quantum systems. The known for the weighted entropy information inequality (subadditivity condition) is extended to the case of indivisible…
Following [1], the aim of this paper is to analyze the relative weighted entropy involving the central moments weight functions. We compare the standard relative entropy with the weighted case in two particular forms of Gaussian…
We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted…
Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks. In the previous work (Xu et al, 2016 \cite{xu2016}), we measure the contribution of a path in link prediction with…
It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…
For a certain moment, the information volume represented in a probability space can be accurately measured by Shannon entropy. But in real life, the results of things usually change over time, and the prediction of the information volume…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…
We consider a random field $\phi(\mathbf{r})$ in $d$ dimensions which is largely concentrated around small `hotspots', with `weights', $w_i$. These weights may have a very broad distribution, such that their mean does not exist, or else is…
In this paper, we study the properties of the weighted entropy generating function (WEGF). We also introduce the weighted residual entropy generating function (WREGF) and establish some characterization results based on its connections with…
Often the rows (cases, objects) of a dataset have weights. For instance, the weight of a case may reflect the number of times it has been observed, or its reliability. For analyzing such data many rowwise weighted techniques are available,…
The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have…
The authors have recently defined the R\'enyi information dimension rate $d(\{X_t\})$ of a stationary stochastic process $\{X_t,\,t\in\mathbb{Z}\}$ as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the…