Spectral Ranking of Causal Influence in Complex Systems

12/24/2020 ∙ by Errol Zalmijn, et al. ∙ 0

Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of data remain a major challenge to effectively diagnose rare or new system issues by merely using model-based approaches. To reduce the causal search space, we validate an algorithm that applies transfer entropy to obtain a weighted directed graph from a system's multivariate time series and graph eigenvector centrality to identify the system's most influential parameters. The results suggest that this approach robustly identifies the true influential sources in a complex system, even when its information transfer network includes redundant edges.

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References

  • Schreiber [2000] T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85, 461–464 (2000).
  • Barnett et al. [2009] L. Barnett, A. B. Barrett, and A. K. Seth, Granger causality and transfer entropy are equivalent for gaussian variables., Phys. Rev. Lett. 103, 238701 (2009).
  • Bonacich [1972] P. Bonacich, Factoring and weighting approaches to status scores and clique identification, Journal of Mathematical Sociology 2, 113 (1972).
  • Wiener [1956] N. Wiener, The theory of prediction, modern mathematics for the engineer, Modern Mathematics for the Engineer , 165–187 (1956).
  • Schreiber and Schmitz [2000] T. Schreiber and A. Schmitz, Surrogate time series, Physica D: Nonlinear Phenomena 142, 346–382 (2000).
  • Page et al. [1998] L. Page, S. Brin, R. Motwani, and T. Winograd, The pagerank citation ranking: Bringing order to the web, Technical report, Stanford Digital Libraries , 1 (1998).
  • Frobenius [1912] G. Frobenius, Ueber matrizen aus nicht negativen elementen, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 26, 456–477 (1912).
  • Perron [1907] O. Perron, Zur theorie der matrices, Mathematische Annalen 2, 248–263 (1907).
  • Wills [2006] R. S. Wills, Google’s pagerank: The math behind the search engine, The Mathematical Intelligencer 28, 6 (2006).
  • von Mises and Pollaczek-Geiringer [1929] R. von Mises and H. Pollaczek-Geiringer, Praktische verfahren der gleichungsauflösung, ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 9, 152 (1929).
  • Kalavri et al. [2016] V. Kalavri, T. Simas, and D. Logothetis, The shortest path is not always a straight line: Leveraging semimetricity in graph analysis, Proc. VLDB Endow. 9, 672 (2016).
  • Wibral et al. [2012]

    M. Wibral, P. Wollstadt, U. Meyer, N. Pampu, V. Priesemann, and R. Vicente, Revisiting wiener’s principle of causality — interaction-delay reconstruction using transfer entropy and multivariate analysis on delay-weighted graphs, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology , 3676 (2012).

  • Flunkert [2011] V. Flunkert, Pydelay: A simulation package, delay-coupled complex systems: and applications to lasers, Springer-Verlag Berlin Heidelberg  (2011).
  • Streicher and Sandrock [2019] S. Streicher and C. Sandrock, Plant-wide fault and disturbance screening using combined transfer entropy and eigenvector centrality analysis, arXiv:1904.04035  (2019).
  • Runge [2018] J. Runge, Causal network reconstruction from time series: From theoretical assumptions to practical estimation, Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 075310 (2018).
  • Lizier [2014] J. T. Lizier, Jidt: An information-theoretic toolkit for studying the dynamics of complex systems, Frontiers in Robotics and AI 1, 11 (2014).
  • Bauer [2005] M. Bauer, Data-driven methods for process analysis. doctoral thesis, University of London.  (2005).
  • Gencaga et al. [2015] D. Gencaga, W. Rossow, and K. Knuth, A recipe for the estimation of information flow in a dynamical system, Entropy 17, 438 (2015).
  • Coufal et al. [2017] D. Coufal, J. Jakubík, J. N., J. Hlinka1, A. Krakovská, and M. Paluš, Detection of coupling delay: A problem not yet solved, Chaos 27, 083109 (2017).
  • Rayleigh [1916] L. Rayleigh, On convecting currents in a horizontal layer of fluid when the higher temperature is on the under side, Philos. Mag. 32, 529–546 (1916).