Kernel method for nonlinear granger causality.

By Daniele Marinazzo, Mario Pellicoro, Sebastiano Stramaglia. Physical Review Letters, 2007

373 citations recorded by the source corpus.

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Subfields: Artificial Intelligence, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a42c36171a6794943ab310f55dd0e4c577cca2e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Anil K. Seth
2. K. Müller
3. Guido Nolte
4. Steven L. Bressler
5. Stefan Haufe
6. Vadim V. Nikulin
7. Wojciech Samek
8. Grgoire Montavon

In Economics and Econometrics

1. K. Müller
2. Anil K. Seth
3. Steven L. Bressler
4. Patrick Meyfroidt
5. A. Baker

In Statistical and Nonlinear Physics

1. Steven L. Bressler
2. K. Müller
3. Anil K. Seth
4. Mark Newman
5. Alessandro Vespignani
6. Duncan J. Watts
7. Grgoire Montavon
8. Kyunghyun Cho

Citations in the corpus

• A critical assessment of connectivity measures for EEG data: A simulation study (2013, background): “There exists also nonlinear variants of Granger causality (Marinazzo et al., 2008; Vicente et al., 2011), which are not considered here.”
• Detecting Causality in Complex Ecosystems (2012, methodology): “(52) apply Granger’s criterion to nonlinear systems using a kernel-based approach (that is similar to the Sugihara (53) S-map) to coprediction.”
• Wiener-Granger Causality: A well established methodology (2011, positive): “Specific implementations of nonlinear WGC include a kernel-based method (Ancona et al., 2004; Marinazzo et al., 2008) which is suggested to be well suited to short and noisy time series.”