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The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the…

Information Theory · Computer Science 2025-09-19 Frank Nielsen

There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leiber's (1951)relative information and Jeffreys (1946) J-divergence, Information…

Probability · Mathematics 2007-05-23 Inder Jeet Taneja

We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as…

Information Theory · Computer Science 2019-10-08 Frank Nielsen , Gaëtan Hadjeres

This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…

Machine Learning · Computer Science 2020-12-11 Vincenzo Bonnici

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja arithemtic-geometric…

Information Theory · Computer Science 2011-09-27 Inder Jeet Taneja

This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…

Probability · Mathematics 2025-10-31 Xinpeng Li , Miao Yu

In this paper we have considered a single inequality having 11 known divergence measures. This inequality include measures like: Jeffryes-Kullback-Leiber J-divergence, Jensen-Shannon divergence (Burbea-Rao, 1982), arithmetic-geometric mean…

Information Theory · Computer Science 2012-05-08 Inder Jeet Taneja

The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…

Mathematical Physics · Physics 2008-01-23 Attila Andai

Analyzing correlation between variables is often both the tool and the goal of modern science. A crucial question is whether the correlation between two variables is a direct correlation or only an indirect correlation through a confounder.…

Methodology · Statistics 2026-04-22 Shengjun Wu , Jeffery Wu

We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…

Quantum Physics · Physics 2023-07-19 Diego G. Bussandri , Pedro W. Lamberti , Karol Życzkowski

There are three classical divergence measures known in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber \cite{jef} \cite{kul} \textit{J-divergence}. Sibson-Burbea-Rao \cite{sib} \cite{bur1,…

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

The one parameter family of Jack(alpha) measures on partitions is an important discrete analog of Dyson's beta ensembles of random matrix theory. Except for special values of alpha=1/2,1,2 which have group theoretic interpretations, the…

Combinatorics · Mathematics 2007-05-23 Jason Fulman

We generalize the family of $\alpha$-divergences using a pair of strictly comparable weighted means. In particular, we obtain the $1$-divergence in the limit case $\alpha\rightarrow 1$ (a generalization of the Kullback-Leibler divergence)…

Information Theory · Computer Science 2022-11-23 Frank Nielsen

We introduce a novel parametric family of symmetric information-theoretic distances based on Jensen's inequality for a convex functional generator. In particular, this family unifies the celebrated Jeffreys divergence with the…

Computer Vision and Pattern Recognition · Computer Science 2011-12-20 Frank Nielsen

Jim\'enez, Becerra, and Gelbukh (2013) defined a family of "symmetric Tversky ratio models" $S_{\alpha,\beta}$, $0\le\alpha\le 1$, $\beta>0$. Each function $D_{\alpha,\beta}=1-S_{\alpha,\beta}$ is a semimetric on the powerset of a given…

Metric Geometry · Mathematics 2022-12-08 Bjørn Kjos-Hanssen

In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…

Information Theory · Computer Science 2011-05-02 Inder Jeet Taneja

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

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the…

Information Theory · Computer Science 2021-04-27 Masanari Kimura , Hideitsu Hino

We examine the problem of controlling divergences for latent space regularisation in variational autoencoders. Specifically, when aiming to reconstruct example $x\in\mathbb{R}^{m}$ via latent space $z\in\mathbb{R}^{n}$ ($n\leq m$), while…

Machine Learning · Computer Science 2021-01-05 Jacob Deasy , Nikola Simidjievski , Pietro Liò

Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible…

Mathematical Physics · Physics 2012-10-16 Saeid Molladavoudi , Hishamuddin Zainuddin , Chan Kar Tim