Related papers: Inequalities Among Symmetric Divergence Measures a…
We extend the trace-logarithmic $S$-divergence from matrices to tracial $C^*$-algebras and finite von Neumann algebras, and show that its square root defines a metric on the invertible positive cone. We also prove an integral representation…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
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…
We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides further…
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…
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. It contains as particular cases the famous means such as harmonic, geometric, arithmetic, etc. Also it contains, the power mean of…
We introduce a novel family of distances, called the chord gap divergences, that generalizes the Jensen divergences (also called the Burbea-Rao distances), and study its properties. It follows a generalization of the celebrated statistical…
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…
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…
I. Sason obtained the tight bounds for symmetric divergence measures are derived by applying the results established by G. L. Gilardoni. In this article, we are going to report two kinds of extensions for the above results, namely classical…
Masked Language Models (MLMs) have been successful in many natural language processing tasks. However, real-world stereotype biases are likely to be reflected in MLMs due to their learning from large text corpora. Most of the evaluation…
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…
In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum…
We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables
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…
Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…
Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma…
We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and…
Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can…