相关论文: Nonextensive Generalizations of the Jensen-Shannon…

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,…

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability…

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…

In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability…

The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence…

In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's…

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 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 inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…

Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the…

The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the…

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…

Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…

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…

The effect of nonextensivity of self-gravitating systems on the Jeans criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized…

There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leibler (1951) relative information and Jeffreys (1951) J-divergence. Sibson (1969)…

Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…

We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…