Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

Wismüller, Axel; DSouza, Adora M.; Vosoughi, Mehdi; Abidin, Anas Z.

doi:10.1038/s41598-021-87316-6

Cited by 40 publications

(20 citation statements)

References 43 publications

(69 reference statements)

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“…In connection with (13) we may note that for 0 < α < 1 the multiplicative factor is positive, and so the RTE is negative if by learning Y (l) n the rare events are (on average) more emphasized than in the case when only X (k) n alone is known. Analogically, for α > 1 the RTE can be negative when, by learning Y (l) n , the more probable events are (on average) more accentuated in comparison with the situation when Y (l) n is not known.…”

Section: Escort Distributionmentioning

confidence: 99%

“…Extracting causal interdependencies from observational data is presently one of the key tasks in nonlinear time series analysis. Apart from the linear Granger causality and various nonlinear extensions thereof [11][12][13], existing methods for this purpose include, for instance, state-space based approaches such as conditional probabilities of recurrence [14][15][16], or information-theoretic quantities such as conditional mutual information [17,18] and transfer entropies [2,[19][20][21]. Especially, the latter information-theoretic quantities represent powerful instruments in quantifying causality between time-evolving systems.…”

Section: Introductionmentioning

confidence: 99%

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Causal inference in time series in terms of Rényi transfer entropy

Jizba,

Lavička,

Tabachová

2022

Preprint

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Uncovering causal interdependencies from observational data is one of the great challenges of nonlinear time series analysis. In this paper, we discuss this topic with the help of informationtheoretic concept known as Rényi's information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi's transfer entropy. We show that by choosing Rényi's parameter α appropriately we can control information that is transferred only between selected parts of underlying distributions. This, in turn, provides particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of "black swan" events such as spikes or sudden jumps are of a key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend this results to heavy-tailed α-Gaussian variables. These results allow to establish connection between autoregressive and Rényi entropy based information-theoretic approaches to data-driven causal inference. To aid our intuition we employ Leonenko et al. entropy estimator and analyze Rényi's information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi's transfer entropy not only allowed us to detect a threshold of synchronization but it also provided a non-trivial insight into the structure of a transient regime that exists between region of chaotic correlations and synchronization threshold. In addition, from Rényi's transfer entropy we could reliably infer the direction of coupling -and hence causality, only for coupling strengths smaller that the onset value of transient regime , i.e. when two Rössler systems were coupled, but have not yet entered a synchronization.

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Section: Escort Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Causal inference in time series in terms of Rényi transfer entropy

Jizba,

Lavička,

Tabachová

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Under the Gaussian assumption, transfer entropy is equivalent to Granger causality [11]. However, the computation of multivariate Granger causality for short time series in large-scale problems is challenging [2,[12][13][14][15]. Addressing this challenge, we recently proposed large-scale Extended Granger Causality (lsXGC), which is a method that combines the advantages of dimensionality reduction with the augmentation of a conditional source time-series adopted from the original space.…”

Section: Introductionmentioning

confidence: 99%

Investigation of large-scale extended Granger causality (lsXGC) on synthetic functional MRI data

Wismüller¹,

Vosoughi²,

DSouza³

et al. 2022

Preprint

Self Cite

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It is a challenging research endeavor to infer causal relationships in multivariate observational time-series. Such data may be represented by graphs, where nodes represent time-series, and edges directed causal influence scores between them. If the number of nodes exceeds the number of temporal observations, conventional methods, such as standard Granger causality, are of limited value, because estimating free parameters of time-series predictors lead to underdetermined problems. A typical example for this situation is functional Magnetic Resonance Imaging (fMRI), where the number of nodal observations is large, usually ranging from 10 2 to 10 5 time-series, while the number of temporal observations is low, usually less than 10 3 . Hence, innovative approaches are required to address the challenges arising from such data sets. Recently, we have proposed the large-scale Extended Granger Causality (lsXGC) algorithm, which is based on augmenting a dimensionality-reduced representation of the system's state-space by supplementing data from the conditional source time-series taken from the original input space. Here, we apply lsXGC on synthetic fMRI data with known ground truth and compare its performance to state-of-the-art methods by leveraging the benefits of information-theoretic approaches. Our results suggest that the proposed lsXGC method significantly outperforms existing methods, both in diagnostic accuracy with Area Under the Receiver Operating Characteristic (AUROC = 0.849 vs. [0.727, 0.762] for competing methods, p < 10 −8 ), and computation time (3.4 sec vs. [9.7, 4.8 × 10 3 ] sec for competing methods) benchmarks, demonstrating the potential of lsXGC for analyzing large-scale networks in neuroimaging studies of the human brain.

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“…However, the latent causal relationships between components of these systems are hidden. To understand network dynamics one must infer causal relations from the available time-based observational data [24]. Time series causality inference quantifies the degree to which one variable evolution in time impacts another variable trajectory.…”

Section: Related Workmentioning

confidence: 99%

“…More recently [24], [15] and [18] proposed causality frameworks that account for network nonlinearities. Large-scale nonlinear Granger causality (lsNGC) [24] models high dimensional limited-time series interval data with nonlinear dimensionality reduction techniques using radial basis functions to identify statistically significant casual relations. lsNGC is applied to functional Magnetic Resonance Imaging (fMRI) data to detect causality in brain tissues.…”

Section: Related Workmentioning

confidence: 99%

Learning Gene Regulatory Networks using Graph Granger Causality

Patil¹,

Vaida²

EPiC Series in Computing

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Interacting systems such as gene regulatory networks have the ability to respond to in- dividual component changes, propagate these changes throughout the network, and affect the temporal trajectories of other network elements. Causality techniques are frequently employed to investigate the interconnection between variables in complex dynamical sys- tems. However, the vast majority of causality models are rooted in regression techniques such as Vector Autoregression Models and Bootstrap Elastic net regression from Time Se- ries framework, and there is very limited research in the space of deep learning, particularly graph neural networks. In this paper, we explore in more depth the concept of Granger causality in deep learning and propose Granger causality deep learning framework using graphs convolutions, LSTM, and nonlinear penalties for the objective of learning causal relationships between temporal elements in gene regulatory networks. The deep learn- ing architecture proposed here for studying causality in dynamic networks has achieved high results on simulated networks as well as on more challenging Dream3 gene regulatory networks time-series datasets.

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Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

Cited by 40 publications

References 43 publications

Causal inference in time series in terms of Rényi transfer entropy

Causal inference in time series in terms of Rényi transfer entropy

Investigation of large-scale extended Granger causality (lsXGC) on synthetic functional MRI data

Learning Gene Regulatory Networks using Graph Granger Causality

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