Related papers: Generalized Symmetric Divergence Measures and Metr…
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
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…
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…
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…
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…
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…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
Metrics on Grassmannians have a wide array of applications: machine learning, wireless communication, computer vision, etc. But the available distances between subspaces of distinct dimensions present problems, and the dimensional asymmetry…
G\"ahler ([3],[4]) introduced the concept of 2-metric as a possible generalization of usual notion of a metric space. In many cases the results obtained in the usual metric spaces and 2-metric spaces are found to be unrelated (see [5]).…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
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…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a…
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…
From geometrical point of view, Eve (2003) studied seven means. These means are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal mean. We have considered for the first time a new measure calling…
The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain…
Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
In a series of papers in the 1960's, S. G\"ahler defined and investigated so-called m-metric spaces and their topological properties. An m-metric assigns to any tuple of m+1 elements a real value (more generally an element in a partially…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…