Related papers: $f$-divergence Inequalities
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Smooth Csisz\'ar $f$-divergences can be expressed as integrals over so-called hockey stick divergences. This motivates a natural quantum generalization in terms of quantum Hockey stick divergences, which we explore here. Using this recipe,…
We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…
The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
Inequality measures provide a valuable tool for the analysis, comparison, and optimization based on system models. This work studies the relation between attributes or features of an individual to understand how redundant, unique, and…
We study convexity properties of R\'{e}nyi entropy as function of $\alpha>0$ on finite alphabets. We also describe robustness of the R\'{e}nyi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on…
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…