Related papers: Time-irreversibility tests for random-length time …
In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
We introduce estimators for the entropy production of a Gibbsian process based on the observation of a single or two typical trajectories. These estimators are built with adequate hitting and return times. We then study their convergence…
Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received an increasing attention during the last decades, thanks to the information…
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…
We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop…
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…
We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
This paper presents a statistical parser for natural language that obtains a parsing accuracy---roughly 87% precision and 86% recall---which surpasses the best previously published results on the Wall St. Journal domain. The parser itself…
For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE's) time discretization numerical schemes usually destroy the property of…
Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on $S$ elements with independent samples, [Paninski2004] showed…
The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…