Related papers: Some Generalized Information and Divergence Genera…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
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 R\'{e}nyi cross-entropy measure between two distributions, a generalization of the Shannon cross-entropy, was recently used as a loss function for the improved design of deep learning generative adversarial networks. In this work, we…
We extend the Rate-Distortion-Perception (RDP) framework to the R\'enyi information-theoretic regime, utilizing Sibson's $\alpha$-mutual information to characterize the fundamental limits under distortion and perception constraints. For…
In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\'enyi entropies, as descriptors of electronic correlation. By establishing a…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
The R\'enyi information measures are characterized in terms of their Shannon counterparts, and properties of the former are recovered from first principle via the associated properties of the latter. Motivated by this characterization, a…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
R\'enyi transfer entropy (RTE) is a generalization of classical transfer entropy that replaces Shannon's entropy with R\'enyi's information measure. This, in turn, introduces a new tunable parameter $\alpha$, which accounts for sensitivity…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…
This paper considers an information bottleneck problem with the objective of obtaining a most informative representation of a hidden feature subject to a R\'enyi entropy complexity constraint. The optimal bottleneck trade-off between…
This paper proposes $\alpha$-GAN, a generative adversarial network using R\'{e}nyi measures. The value function is formulated, by R\'{e}nyi cross entropy, as an expected certainty measure incurred by the discriminator's soft decision as to…
We study a generalized version of Wyner's common information problem (also coined the distributed source simulation problem). The original common information problem consists in understanding the minimum rate of the common input to…
In this paper we derive explicit formulas of the R\'enyi information, Shannon entropy and Song measure for the invariant density of one dimensional ergodic diffusion processes. In particular, the diffusion models considered include the…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
We discuss two families of two-parameter entropies and divergences, derived from the standard R\'enyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions.…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…