Identifying causal gateways and mediators in complex spatio-temporal systems

Runge, Jakob; Petoukhov, Vladimir; Donges, Jonathan F.; Hlinka, Jaroslav; Jajcay, Nikola; Vejmelka, Martin; Hartman, David; Marwan, Norbert; Paluš, Milan; Kurths, Jüergen

doi:10.1038/ncomms9502

Cited by 238 publications

(257 citation statements)

References 65 publications

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“…Beyond this, our framework might also be applicable to networks constructed from non-pairwise interdependencies that are investigated in, e.g, causal effect networks [74,85,86]. The assessment of statistical complexity could help to more objectively choose thresholds for the construction of such networks and complements existing approaches based on, e.g., the assessment of the recurrence network's percolation threshold [76,87,88].…”

Section: Threshold-based Networkmentioning

confidence: 99%

Mapping and discrimination of networks in the complexity-entropy plane

et al. 2017

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Complex networks are usually characterized in terms of their topological, spatial, or informationtheoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged pernode entropic measure characterizing the network's information content and the associated JensonShannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

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Section: Threshold-based Networkmentioning

confidence: 99%

Mapping and discrimination of networks in the complexity-entropy plane

et al. 2017

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“…These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].…”

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Pairwise network information and nonlinear correlations

2016

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Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated, or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples. Pairwise measures of dependence such as crosscorrelations (as measured by the Pearson correlation coefficient or covariance matrix) and mutual information are widely used to characterize the interactions within complex systems. They are a key ingredient to techniques such as principal component analysis, empirical orthogonal functions, and functional networks (networks inferred from dynamical time series) [1][2][3]. These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].In this paper we study how faithfully these measures alone can represent a given system. With the increasing use of functional networks this topic has received much attention recently, and many technical concerns have been brought to light dealing with the inference of these networks. Previous studies have shown that the estimates of the functional networks can be negatively affected by properties of the time series [9][10][11], as well as properties of the measure of association, e.g. crosscorrelations [12][13][14][15]. In this work however, we address a more fundamental question: How well do pairwise measurements represent a system?In principle this can be evaluated using a maximum entropy approach. The corresponding framework was first laid out in [16] and later applied in [17], where they assessed the rationale of only looking at the pairwise correlations between neurons. They examined how well the maximum entropy distribution, consistent with all the pairwise correlations described...

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“…Note, however, that reliable causal analyses, especially with information-theoretic estimators, require much more samples than classical bivariate analysis, which typically restricts their applicability to much smaller networks. 88 An alternative to classical path-based network measures is discussed by Runge et al 89 and Runge, 90 and introduces quantifiers of information transfer through causal pathways.…”

Section: Discussion and Extensionsmentioning

confidence: 99%

“…20 It has been already successfully used in a wide variety of applications, ranging from the complex structure of teleconnections in the climate system, 15,18,49 including backbones and bottlenecks, 19,89 to dynamics and predictability of the El Niño-Southern Oscillation (ENSO). 66,92,93 Climate networks (class climate.ClimateNetwork) represent strong statistical interrelationships between time series and are typically reconstructed by thresholding the matrix of a statistical similarity measure S (Fig.…”

Section: B Climate Networkmentioning

confidence: 99%

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

Donges

Heitzig

Beronov

et al. 2015

Chaos

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We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni-and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Network theory and nonlinear time series analysis provide powerful tools for the study of complex systems in various disciplines such as climatology, neuroscience, social science, infrastructure or economics. In the last years, combining both frameworks has yielded a wealth of new approaches for understanding and modeling the structure and dynamics of such systems based on the statistical analysis of network or uni-and multivariate time series. The pyunicorn software package (available at https://github.com/pik-copan/pyunicorn) facilitates the innovative synthesis of methods from network theory and nonlinear time series analysis in order to develop novel integrated methodologies. This paper provides an overview of the functionality provided by pyunicorn, introduces the theoretical concepts behind it and provides examples in the form of selected use cases mainly in the fields of climatology and paleoclimatology.

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Identifying causal gateways and mediators in complex spatio-temporal systems

Cited by 238 publications

References 65 publications

Mapping and discrimination of networks in the complexity-entropy plane

Mapping and discrimination of networks in the complexity-entropy plane

Pairwise network information and nonlinear correlations

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

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Identifying causal gateways and mediators in complex spatio-temporal systems

Cited by 238 publications

References 65 publications

Mapping and discrimination of networks in the complexity-entropy plane

Mapping and discrimination of networks in the complexity-entropy plane

Pairwise network information and nonlinear correlations

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

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Product

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Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package