Abstract
In this paper, we propose a novel definition of Wiener causality to describe the intervene between time series, based on relative entropy. In comparison to the classic Granger causality, by which the interdependence of the statistic moments beside the second moments are concerned, this definition of causality theoretically takes all statistic aspects into considerations. Furthermore under the Gaussian assumption, not only the intervenes between the co-variances but also those between the means are involved in the causality. This provides an integrated description of statistic causal intervene. Additionally, our implementation also requires minimum assumption on data, which allows one to easily combine modern predictive model with causality inference. We demonstrate that REC outperform the standard causality method on a series of simulations under various conditions.
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Notes
- 1.
For the case of high dimensions, the similar results can be derived by the same fashion.
- 2.
Also as \(GC_{y\rightarrow x}=\ln \{\mathrm{tr}[\varSigma (x|x^{p})]/\mathrm{tr}[\varSigma (x|x^{p}\oplus y^{q})]\}\).
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Acknowledgments
This work is jointly supported by the National Natural Sciences Foundation of China under Grant No. 61673119, the Key Program of the National Science Foundation of China No. 91630314, the Laboratory of Mathematics for Nonlinear Science, Fudan University, and the Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University.
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Chen, J., Feng, J., Lu, W. (2018). A Wiener Causality Defined by Relative Entropy. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11302. Springer, Cham. https://doi.org/10.1007/978-3-030-04179-3_11
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