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In this paper we introduce the intuitive notion of trivergence of probability distributions (TPD). This notion allow us to calculate the similarity among triplets of objects. For this computation, we can use the well known measures of…

Information Theory · Computer Science 2015-06-23 Juan-Manuel Torres-Moreno

This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…

Methodology · Statistics 2014-01-13 Sueli I. R. Costa , Sandra A. Santos , João E. Strapasson

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

Information Theory · Computer Science 2011-03-29 Inder Jeet Taneja

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which include the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence…

Statistics Theory · Mathematics 2019-04-01 Ba Amadou Diadie , Gane Samb Lo

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Information Theory · Computer Science 2026-05-28 Yanxiao Liu , Yijun Fan , Deniz Gündüz

We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler…

Probability · Mathematics 2021-12-17 Arnaud Marsiglietti , Puja Pandey

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

Methodology · Statistics 2017-04-18 Gane Samb Lo , Amadou Diadié Ba , Diam Ba

Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…

Information Theory · Computer Science 2016-11-15 Igal Sason

We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and…

Information Theory · Computer Science 2021-04-16 Frank Nielsen

This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…

Statistics Theory · Mathematics 2024-10-07 Lasse Leskelä

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Statistics Theory · Mathematics 2022-03-03 Michel Broniatowski , Wolfgang Stummer

Using Blackwell's definition of comparing two experiments, a comparison is made with \textit{generalized AG - divergence} measure having one and two scalar parameters. Connection of \textit{generalized AG - divergence} measure with…

Statistics Theory · Mathematics 2007-06-13 Inder Jeet Taneja

In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some…

Statistics Theory · Mathematics 2018-09-21 Tomohiro Nishiyama

This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…

Probability · Mathematics 2014-07-04 Eugene A. Feinberg , Pavlo O. Kasyanov , Michael Z. Zgurovsky

$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…

Statistics Theory · Mathematics 2023-10-13 Sreejith Sreekumar , Ziv Goldfeld , Kengo Kato

We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or…

Machine Learning · Computer Science 2023-09-11 Robert C. Williamson , Zac Cranko

We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…

Information Theory · Computer Science 2021-01-05 Yan Wang

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed,…

Quantum Physics · Physics 2009-05-14 Jop Briët , Peter Harremoës

The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the…

Information Theory · Computer Science 2020-10-01 Frank Nielsen

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…

Information Theory · Computer Science 2016-11-17 Igal Sason