Escaping the curse of dimensionality in estimating multivariate transfer entropy.
By Jakob Runge, J. Heitzig, V. Petoukhov, Jürgen Kurths. Physical Review Letters, 2012
313 citations recorded by the source corpus.
Multivariate transfer entropy (TE) is a model-free approach to detect causalities in multivariate time series. It is able to distinguish direct from indirect causality and common drivers without assuming any underlying model. But despite these advantages it has mostly been applied in a bivariate setting as it is hard to estimate reliably in high dimensions since its definition involves infinite vectors. To overcome this limitation, we propose to embed TE into the framework of graphical models and present a formula that decomposes TE into a sum of finite-dimensional contributions that we call decomposed transfer entropy. Graphical models further provide a richer picture because they also yield the causal coupling delays. To estimate the graphical model we suggest an iterative algorithm, a modified version of the PC-algorithm with a very low estimation dimension. We present an appropriate significance test and demonstrate the method's performance using examples of nonlinear stochastic delay-differential equations and observational climate data (sea level pressure).
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/8ac1ea5e041dcf5c6364de9733d2e84cdaf99abb
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Citations in the corpus
- Granger Causality: A Review and Recent Advances (2021, background): “These approaches also suffer from curse of dimensionality (Runge et al., 2012), making them inappropriate in high-dimensional settings.”
- HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity (2013, methodology): “Besides, if the number of variables is high, it may better to use a recently derived method based on probabilistic graphic models (Runge et al. 2012a,b), which has been shown to outperform PTE in distinguishing direct from indirect connections in multivariate data sets.”
- Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings (2014, background): “It can be challenging to do such a test in practice and often times one can instead use a shuffle test to obtain approximate confidence intervals [14].”
- Detecting and quantifying causal associations in large nonlinear time series datasets (2017, unknown): “Causal discovery aims to unveil such spurious dependencies, leading to estimated causal networks that are, therefore, much sparser than correlation networks. for this example, that is, we test ( Nino t − , BCT t ∣ X t − ∖ { Nino t − }) ≠ 0 for different lags , which is the effect size for…”
- Neural Granger Causality (2021, background): “These approaches also suffer from a curse of dimensionality [22] when the number of series grows, making them inappropriate in the high-dimensional setting.”
- Causal network reconstruction from time series: From theoretical assumptions to practical estimation. (2018, methodology): “Many current methods are advancements of the concept of transfer entropy (Wibral et al., 2013; Staniek and Lehnertz, 2008; Vejmelka and Palus, 2008), in particular in its multivariate version (Sun and Bollt, 2014; Sun et al., 2015; Runge et al., 2012b; 2012a; Runge, 2015).”
- p-Causality: Identifying Spatiotemporal Causal Pathways for Air Pollutants with Urban Big Data (2016, background): “There are also various extensions that incorporate spatiotemporal dependencies in the domain of traffic [4], climate [25][26][27] and flood prediction [28].”