Related papers: A Comparative Analysis on the Applicability of Ent…
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…
The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…
We introduce a variant of the R\'enyi entropy definition that aligns it with the well-known H\"older mean: in the new formulation, the r-th order R\'enyi Entropy is the logarithm of the inverse of the r-th order H\"older mean. This brings…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…
R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
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 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…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…
In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…