Related papers: Estimation of Tsallis entropy for exponentially di…

The optimization problems defining meta-stable or stationary equilibrium are explored. The Gibbs scheme is modified aiming to describe the statistical properties of a class of non-equilibrium and metastable states. The system is assumed to…

The local structure entropy is a new method which is proposed to identify the influential nodes in the complex networks. In this paper a new form of the local structure entropy of the complex networks is proposed based on the Tsallis…

This paper 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 a Poisson random…

This paper proposes a new method for estimating the joint probability mass function of a pair of discrete random variables. This estimator is used to construct joint Shannon R\'enyi-Tsallis entropies, and the mutual information estimates of…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

We demonstrate and discuss the process of gaining information and show an example in which some specific way of gaining information about an object results in the Tsallis form of entropy rather than in the Shannon one.

The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems…

We explore a supervised machine learning approach to estimate the entanglement entropy of multi-qubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's…

A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the…

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…

We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…

The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…

It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…

This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…

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 study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which…