Related papers: Assessing coupling dynamics from an ensemble of ti…
Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since…
This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
In this manuscript we present a comparative study about the determination of the relaxation (\textit{i.e.}, independence) time scales obtained from the correlation function, the mutual information, and a criterion based on the evaluation of…
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…
Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…
The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
This work uses an information-based methodology to infer the connectivity of complex systems from observed time-series data. We first derive analytically an expression for the Mutual Information Rate (MIR), namely, the amount of information…
We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after…
A model-free measure of coupling between dynamical variables is built from time series embedding principle. The approach described does not require a mathematical form for the dynamics to be assumed. The approach also does not require…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…