Related papers: Mathematical inequalities for some divergences
A probabilistic rationale for I-divergence minimization (relative entropy maximization), non-parametric likelihood maximization and J-divergence minimization (Jeffres' entropy maximization) criteria is provided.
We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
Tsallis and R\'{e}nyi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under suitable constraints, leads to the $q$-exponential family…
In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $\chi ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
Information divergences allow one to assess how close two distributions are from each other. Among the large panel of available measures, a special attention has been paid to convex $\varphi$-divergences, such as Kullback-Leibler,…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
Coherence is the most fundamental quantum feature of the nonclassical systems. The understanding of coherence within the resource theory has been attracting increasing interest among which the quantification of coherence is an essential…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…
The Bakry-\'Emery $\Gamma_2$ criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-\'Emery $\Gamma_2$ criterion inequalities which in the limit case…
The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss…
In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend…
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss…
In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
We investigate the gravitational origin of the Tsallis entropy, characterized by the nonadditive index $\delta$. Utilizing Wald's formalism within the framework of $f(R)$ modified theories of gravity, we evaluate the entropy on the black…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.