Related papers: A Scale-Invariant Entropy Statistic for Distance D…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. Motivated by shell model observations, we develop a similarity theory for the inertial…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
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…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…
We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 90's. We show that it is a metric invariant indeed and calculate it in several special cases.