Related papers: A Comparative Analysis on the Applicability of Ent…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We show that the R\'enyi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, $S_{n}$, where $|n|<1$, it is…
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We…
Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…
Mobile sensor data has been proposed for security-critical applications such as device pairing, proximity detection, and continuous authentication. However, the foundational premise that these signals provide sufficient entropy remains…
Approximation of entropies of various types using machine learning (ML) regression methods are shown for the first time. The ML models presented in this study define the complexity of the short time series by approximating dissimilar…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
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…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…
Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…