Informational divergence and the dissimilarity of probability distributions

Sgarro, Andrea

doi:10.1007/bf02576360

Cited by 23 publications

(17 citation statements)

References 4 publications

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“…Mixed f -divergence, which is important in applications, such as statistical hypothesis testing and classification, see e.g., [35,40,61], measures the difference between multiple pairs of (probability) distributions. Examples include, e.g., the Matusita's affinity [33,34], the Toussaint's affinity [51], the information radius [48] and the average divergence [47]. Mixed f -divergence is an extension of the classical f -divergence and can be viewed as a vector form of classical f -divergence.…”

Section: Introductionmentioning

confidence: 99%

Mixedf-divergence and inequalities for log-concave functions

Caglar

Werner

2014

Proceedings of the London Mathematical Society

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Mixed f -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions.Special cases of f -divergences are mixed L λ -affine surface areas for log concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santaló type inequality.

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Section: Introductionmentioning

confidence: 99%

Mixedf-divergence and inequalities for log-concave functions

Caglar

Werner

2014

Proceedings of the London Mathematical Society

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“…The Jensen-Shannon divergence (JSD) based on Kullback-Leibler divergence [9][10][11][12] is used to measure the similarity between two probability distributions. Let 𝐾(𝑃, 𝑄) be Kullback-Leibler divergence, then the Jensen-Shannon divergence is written in terms of Kullback-Leibler divergence is…”

Section: Departure From the Qua Modelmentioning

confidence: 99%

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Aktaş

Yılmaz

2021

Mugla Journal of Science and Technology

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The Uniform Association (UA) and Quasi-Uniform Association (QUA) models are used for analysis of two-way square contingency tables with ordered categories. When the QUA model does not fit the data, one wants to measure the degree of departure from the quasi-uniform association model. The degree of the departure from the model is calculated by using the power divergence statistics. In this study, as an alternative to measures in the literature, a measure to estimate the degree of departure from the QUA model is suggested. This suggested measure allows us to compare the several R×R tables in terms of the departure from the model. The measures are compared by the simulation study and discussed by three unaided distance vision data.

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“…In this section we shall relate R-divergence parametric measures t V r s (θ) (t = 1 and 2) given by (4) to the Fisher's information measure I F X (θ) given by (5).…”

Section: Fisher Measure Of Information and Generalized R-divergence Measuresmentioning

confidence: 99%

“…Furthermore, the measure arising owing to concavity of Shannon's entropy known as information Radius [3], is also gaining importance towards applications. There exists a beautiful inequality [4,5] between information radius and J-divergence. Burbea and Rao [4,6] called information radius as Jensen difference divergence measure and also presented its one scalar parametric generalization.…”

Section: Introductionmentioning

confidence: 99%

Generalized Jensen difference divergence measures and Fisher measure of information

1995

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IntroductionSeveral measures have been introduced in the literature on information theory and statistics as measures of information. The most commonly used in information theory is Shannon's entropy [1]. It gives the amount of uncertainty concerning the outcome of an experiment. Kullback and Leibler[2] introduced a measure associated with two distributions of an experiment. It expresses the amount of information supplied by the data for discriminating among the distributions. As symmetric measure, the Jeffreys-Kullback-Leibler J-divergence is commonly used. Furthermore, the measure arising owing to concavity of Shannon's entropy known as information Radius [3], is also gaining importance towards applications. There exists a beautiful inequality [4,5] between information radius and J-divergence. Burbea and Rao[4,6] called information radius as Jensen difference divergence measure and also presented its one scalar parametric generalization. Some properties and applications of Jensen difference divergence measure and its generalizations can be seen in [4,[6][7][8][9][10]. Recently, Taneja[11] introduced different ways to generalize Jensen difference divergence measure having two scalar parameters, while two scalar parametric generalizations of J-divergence can be seen in Taneja [11][12][13][14].On the other side, the most famous measure in the literature of statistics is the Fisher's[15] measure of information. It measures the amount of information supplied by the data about an unknown parameter θ. Rao[16] introduced the Riemannian metric in a model of probability distributions by using the Fisher information matrix. C

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Informational divergence and the dissimilarity of probability distributions

Cited by 23 publications

References 4 publications

Mixedf-divergence and inequalities for log-concave functions

Mixedf-divergence and inequalities for log-concave functions

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Generalized Jensen difference divergence measures and Fisher measure of information

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