A symmetric information divergence measure of the Csiszár's f-divergence class and its bounds

Kumar, Pranesh; Chhina, S.

doi:10.1016/j.camwa.2004.07.017

Cited by 16 publications

(12 citation statements)

References 9 publications

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“…Regardless of the outbreak simulated, OSF = 1 can be considered as a kind of threshold below which the loss of information increasingly impairs simulation quality in terms of goodness-of-fit and variance. As an overall measure of simulation GOF, we used and recommend the χ 2 -divergence, which is also a measure of the loss of information during the simulation process [ 49 , 50 ].…”

Section: Resultsmentioning

confidence: 99%

Building test data from real outbreaks for evaluating detection algorithms

et al. 2017

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Benchmarking surveillance systems requires realistic simulations of disease outbreaks. However, obtaining these data in sufficient quantity, with a realistic shape and covering a sufficient range of agents, size and duration, is known to be very difficult. The dataset of outbreak signals generated should reflect the likely distribution of authentic situations faced by the surveillance system, including very unlikely outbreak signals. We propose and evaluate a new approach based on the use of historical outbreak data to simulate tailored outbreak signals. The method relies on a homothetic transformation of the historical distribution followed by resampling processes (Binomial, Inverse Transform Sampling Method—ITSM, Metropolis-Hasting Random Walk, Metropolis-Hasting Independent, Gibbs Sampler, Hybrid Gibbs Sampler). We carried out an analysis to identify the most important input parameters for simulation quality and to evaluate performance for each of the resampling algorithms. Our analysis confirms the influence of the type of algorithm used and simulation parameters (i.e. days, number of cases, outbreak shape, overall scale factor) on the results. We show that, regardless of the outbreaks, algorithms and metrics chosen for the evaluation, simulation quality decreased with the increase in the number of days simulated and increased with the number of cases simulated. Simulating outbreaks with fewer cases than days of duration (i.e. overall scale factor less than 1) resulted in an important loss of information during the simulation. We found that Gibbs sampling with a shrinkage procedure provides a good balance between accuracy and data dependency. If dependency is of little importance, binomial and ITSM methods are accurate. Given the constraint of keeping the simulation within a range of plausible epidemiological curves faced by the surveillance system, our study confirms that our approach can be used to generate a large spectrum of outbreak signals.

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Section: Resultsmentioning

confidence: 99%

Building test data from real outbreaks for evaluating detection algorithms

et al. 2017

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“…Corresponding to Kumar and Chhina [10] divergence measure, we proposed the divergence measure for FSs as follows:…”

Section: New Divergence For Fssmentioning

confidence: 99%

“…In the literature, various information measures have been proposed such that each definition enjoys some definite axiomatic or heuristic postulates, which lead to their extensive applications in different disciplines. A conventional categorization to distinguish these measures is as: parametric, non-parametric, and entropy-type measures of information [10]. Parametric measures determine the amount of information delivered by the object regarding an unknown parameter α and are functions of α.…”

Section: Introductionmentioning

confidence: 99%

Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection

et al. 2020

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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 between two objects. Particularly, the idea of divergence measure for fuzzy sets is significant since it has applications in several areas viz., process control, decision making, image segmentation, and pattern recognition. In this paper, some new fuzzy divergence measures, which are generalizations of probabilistic divergence measures are introduced. Next, we review two different generalizations of the following measures. Firstly, directed divergence (Kullback–Leibler or Jeffrey invariant) and secondly, Jensen difference divergence, based on these measures, we develop a class of unified divergence measures for fuzzy sets (FSs). Then, a method based on divergence measure for fuzzy sets (FSs) is proposed to evaluate the multi-criteria decision-making (MCDM) problems under the fuzzy atmosphere. Lastly, an illustrative example of the recycling job selection problem of sustainable planning of the e-waste is presented to demonstrate the reasonableness and usefulness of the developed method.

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“…Another direct application of the method improves Theorem 34 in [1], which is an upper bound on Rényi's divergence in terms of the variational distance and relative information maximum, while providing a simpler proof for this type of inequality. Vajda's well-known "range of values theorem" (see [7]- [11]) is also recovered as an application.…”

Section: Introductionmentioning

confidence: 99%