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Dr. Jakob Runge

Portrait of Jakob Runge

Now at Imperial College London, Grantham Institute for Climate and the Environment (JSMF Postdoctoral Fellowship)

New version of TiGraMITe (Python script for Time series Graph based Measures of Information Transfer) on github:



Research Interests

Theory: Time Series Analysis using Information Theory

Applications: Climate Data

  • Causality and time series graphs
  • Quantifying causal interaction strength
  • Entropies, conditional mutual information and their estimation
  • Classical linear statistics, partial correlation, auto-regressive models and estimation
  • Investigation of drivers of Indian Monsoon
  • ENSO influence in global climate  

Selected Publications

Jakob Runge, Vladimir Petoukhov, Jonathan F. Donges, Jaroslav Hlinka, Nikola Jajcay, 
Martin Vejmelka, David Hartman, Norbert Marwan, Milan Paluš, and Jürgen Kurths "Identifying causal gateways and mediators in complex spatio-temporal systems" Nature Communications 8, 8502 (2015) URL:

ncomms_picIdentifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth’s climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific–Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.


Jakob Runge, Reik V. Donner, and Jürgen Kurths
"Optimal model-free prediction from multivariate time series"
Physical Review E 91(5), 052909 (2015)

predictionForecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Niño Southern Oscillation. 

Jakob Runge, Vladimir Petoukhov, and Jürgen Kurths
"Quantifying the strength and delay of climatic interactions: 
the ambiguities of cross correlation and a novel measure based on graphical models"
Journal of Climate 27(2), 720-739 (2014)
examples data dictionary, tigramite config file

fig10Lagged cross correlation and regression analysis is commonly used to gain insights into interaction mechanisms between climatological processes, in particular to assess time delays and to quantify the strength of a mechanism. In this article, we show how autocorrelations can lead to misleading conclusions about time delays and also obscure a quantification of the interaction mechanism.  To overcome these possible artifacts, we propose a two-step procedure based on the concept of graphical models recently introduced to climate research. The potential of the approach to quantify interactions between two and more processes is demonstrated by investigating teleconnections of ENSO and the mechanism of the Walker circulation. 


Jakob Runge, Jobst Heitzig, Norbert Marwan, and Jürgen Kurths
"Quantifying Causal Coupling Strength: 
A Lag-specific Measure For Multivariate Time Series Related To Transfer Entropy"
Physical Review E 86, 061121 (2012)
DOI: 10.1103/PhysRevE.86.061121
arXiv:1210.2748 []

example pic of entropy diagramWhile it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information theoretic measures and demonstrate the short-comings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (MIT), as a measure of association that is general, causal and lag-specific, reflects a well interpretable notion of coupling strength and is practically computable.


Jakob Runge, Jobst Heitzig, Vladimir Petoukhov, and Jürgen Kurths
"Escaping the Curse of Dimensionality in Estimating Multivariate Transfer Entropy"
Physical Review Letters 108, 258701 (2012)
DOI: 10.1103/PhysRevLett.108.258701
application example data dictionary, tigramite config file

DTE picMultivariate transfer entropy (TE) is a model-free approach to detect causalities in multivariate time series. But 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).


Bernd Pompe and Jakob Runge
"Momentary Information Transfer as a Coupling Measure of Time Series"
Physical Review E 83, 051122 (2011)
DOI: 10.1103/PhysRevE.83.051122

We propose a method to analyze couplings between two simultaneously measured time series. Our approach is based on conditional mutual sorting information. By setting suitable conditions we first of all consider momentary information in both time series. This enables the detection not only of coupling directions but also delays. Sorting information refers to ordinal properties of time series, which makes the analysis robust with respect to strictly monotonous distortions and thus very useful in the analysis of proxy data in climatology. Fortunately, ordinal analysis is easy and fast to compute. We consider also the problem of reliable estimation from finite time series.



J. Runge
"Quantifying information transfer and mediation along causal pathways in complex systems"
arXiv:1508.03808 [stat.ME]
J. Runge
"On the graph-theoretical interpretation of Pearson correlations in a multivariate process and a novel partial correlation measure"
arXiv:1310.5169v1 [math.ST]

More Publications

J. Runge, M. Riedl, A. Müller, H. Stepan, J. Kurths and N. Wessel
"Quantifying the causal strength of multivariate cardiovascular couplings with momentary information
Physiological Measurement 36, 813 (2015) 
Balasis G., R. V. Donner, S. M. Potirakis, J. Runge, C. Papadimitriou, I. A. Daglis, K. Eftaxias,
and J. Kurths
"Statistical mechanics and information-theoretic perspectives on complexity in the Earth system" 
Entropy special issue "Advances in Applied Statistical Mechanics" 15, 4844-4888 (2013) 
Radebach, A., R. V. Donner, J. Runge, J. F. Donges, and J. Kurths 
"Disentangling different types of El Nino episodes by evolving climate network analysis" 
Physical Review E 88, 052807 (2013)
Schleussner, C. F., J. Runge, J. Lehmann, and A. Levermann
"The role of the North Atlantic overturning and deep-ocean for multi-decadal global-mean-temperature variability" 
Earth System Dynamics 5, 103-115 (2013)
Hlinka, J, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, and M. Paluš
"Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information" 
Entropy 15, 6 (2013)

Older Publication from internship at Lawrence Berkeley National Laboratory

Jakob Runge and B. Grant Logan
"Nonuniformity for Rotated Beam Illumination in Directly Driven Heavy-Ion Fusion"
Physics of Plasmas, 16(033109):1–6 (2009)
DOI: 10.1063/1.3095561.


Jakob Runge, Comment on Wibral et al. (2013): Measuring Information-Transfer Delays (PloS One 2013), pdf

Co-authored scientific reports

H.-J. Schellnhuber et al.: Turn Down the Heat: Climate Extremes, Regional Impacts, and the Case for Resilience.  World Bank Report (2013),  Washington, DC.


TiGraMITe: Python script for Time series Graph based Measures of Information Transfer

Curriculum Vitae on request

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