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A number of simple inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. 1 The weighted Gibbs inequality and its consequences The definition and initial results on weighted entropy were introduced in [1, 14]. Further progress was made, subsequently, in [27, 9, 17, 26, 28, 34, 18],… (More)
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discovery. For discrete-valued samples,… (More)
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. 2000 MSC. 60A10, 60B05, 60C05
We analyse an analog of the entropy-power inequality for the weighted entropy. In particular, we discuss connections with weighted Lieb‘s splitting inequality and an Gaussian additive noise formula. Examples and counterexamples are given, for some classes of probability distributions.
We propose a direct estimation method for Rényi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where η := M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X, Y), we show… (More)
The aim of this paper is to analyze the weighted KyFan inequality proposed in . A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an improvement of the standard KyFan inequality.
We produce a series of results extending information-theoretical inequalities (discussed by Dembo–Cover–Thomas in 1989-1991) to a weighted version of entropy. The resulting inequalities involve the Gaussian weighted entropy; they imply a number of new relations for determinants of positive-definite matrices.
We propose the following definition which we call the double truncated (interval) weighted cumulative residual entropy (IWCRE) IEw φ (t1, t2) and the double truncated (interval) weighted cumulative entropy (IWCE) IE w φ(t1, t2) of a RV X|t1 < X < t2: Department of Statistics, Federal University of São Carlos (UFSCar), São Carlos, Brazil. E-mail:… (More)
In this paper the author analyzes the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions α-th generalized deviation and (α, p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramér-Rao inequalities in terms of generalized Gaussian densities… (More)