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This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The…
This paper addresses the problem of inferring circulation of information between multiple stochastic processes. We discuss two possible frameworks in which the problem can be studied: directed information theory and Granger causality. The…
Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks…
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…
Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience.…
In an intelligent transportation system, the effects and relations of traffic flow at different points in a network are valuable features which can be exploited for control system design and traffic forecasting. In this paper, we define the…
At present, multi-electrode array (MEA) approach and optical recording allow us to acquire plant electrical activity with higher spatio-temporal resolution. To understand the dynamic information flow of the electrical signaling system and…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental…
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such…
The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for…
The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing…
In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent…
Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences,…
We propose a new method of discovering causal relationships in temporal data based on the notion of causal compression. To this end, we adopt the Pearlian graph setting and the directed information as an information theoretic tool for…
Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on…
Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine…
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…