Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2017 (2017), Article ID 4518429, 13 pages
https://doi.org/10.1155/2017/4518429
Research Article

Sparse Causality Network Retrieval from Short Time Series

Tomaso Aste1,2,3 and T. Di Matteo1,2,3,4

1Department of Computer Science, UCL, London, UK
2UCL Centre for Blockchain Technologies, UCL, London, UK
3Systemic Risk Centre, London School of Economics and Political Sciences, London, UK
4Department of Mathematics, King’s College London, London, UK

Correspondence should be addressed to Tomaso Aste

Received 25 May 2017; Accepted 6 September 2017; Published 6 November 2017

Academic Editor: Diego Garlaschelli

Copyright © 2017 Tomaso Aste and T. Di Matteo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Review, vol. 51, no. 1, pp. 34–81, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Theodoridis, Y. Kopsinis, and K. Slavakis, “Sparsity-aware learning and compressed sensing: an overview,” https://arxiv.org/abs/1211.5231.
  3. R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society, Series B, vol. 58, no. 1, pp. 267–288, 1996. View at Google Scholar
  4. W. Barfuss, G. P. Massara, T. Di Matteo, and T. Aste, “Parsimonious modeling with information filtering networks,” Physical Review E, vol. 94, no. 6, Article ID 062306, 2016. View at Google Scholar
  5. T. Aste, T. Di Matteo, and S. T. Hyde, “Complex networks on hyperbolic surfaces,” Physica A: Statistical Mechanics and its Applications, vol. 346, no. 1-2, pp. 20–26, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Tumminello, T. Aste, T. di Matteo, and R. N. Mantegna, “A tool for filtering information in complex systems,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 30, pp. 10421–10426, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. G. P. Massara, T. Di Matteo, and T. Aste, “Network filtering for big data: triangulated maximally filtered graph,” Journal of Complex Networks, vol. 5, no. 2, article 161, 2017. View at Google Scholar
  8. A. Tikhonov, “Solution of incorrectly formulated problems and the regularization method,” Soviet Mathematics Doklady, vol. 4, no. 4, pp. 1035–1038, 1984. View at Google Scholar
  9. A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems,” Technometrics, vol. 12, no. 1, pp. 55–67, 1970. View at Publisher · View at Google Scholar
  10. A. Zaremba and T. Aste, “Measures of causality in complex datasets with application to financial data,” Entropy, vol. 16, no. 4, pp. 2309–2349, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. T. Schreiber, “Measuring information transfer,” Physical Review Letters, vol. 85, no. 2, pp. 461–464, 2000. View at Publisher · View at Google Scholar · View at Scopus
  12. C. E. Shannon, “A mathematical theory of communication,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 5, no. 1, pp. 3–55, 2001. View at Google Scholar
  13. T. W. Anderson, Multivariate Statistical Analysis, Willey and Sons, New York, NY, USA, 1984.
  14. J. Friedman, T. Hastie, and R. Tibshirani, “Sparse inverse covariance estimation with the graphical lasso,” Biostatistics, vol. 9, no. 3, pp. 432–441, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. M. H. Gruber, Improving Efficiency by Shrinkage: The James–Stein and Ridge Regression Estimators, vol. 156 of CRC Press, 1998.
  16. D. M. Witten and R. Tibshirani, “Covariance-regularized regression and classification for high dimensional problems,” Journal of the Royal Statistical Society. Series B. Statistical Methodology, vol. 71, no. 3, pp. 615–636, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. N. Meinshausen and P. Bühlmann, “High-dimensional graphs and variable selection with the lasso,” The Annals of Statistics, vol. 34, no. 3, pp. 1436–1462, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Kruskal Jr., “On the shortest spanning subtree of a graph and the traveling salesman problem,” Proceedings of the American Mathematical Society, vol. 7, no. 1, pp. 48–50, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  19. R. N. Mantegna, “Hierarchical structure in financial markets,” The European Physical Journal B—Condensed Matter and Complex Systems, vol. 11, no. 1, pp. 193–197, 1999. View at Publisher · View at Google Scholar
  20. J. D. Hamilton, Time Series Analysis, vol. 2, Princeton University Press, Princeton, NJ, USA, 1994. View at MathSciNet
  21. S. S. Wilks, “The large-sample distribution of the likelihood ratio for testing composite hypotheses,” The Annals of Mathematical Statistics, vol. 9, no. 1, pp. 60–62, 1938. View at Publisher · View at Google Scholar
  22. Q. H. Vuong, “Likelihood ratio tests for model selection and nonnested hypotheses,” Econometrica. Journal of the Econometric Society, vol. 57, no. 2, pp. 307–333, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  23. J. A. Swets, Signal Detection Theory and ROC Analysis in Psychology and Diagnostics: Collected Papers, Psychology Press, 2014.
  24. I. Varga-Haszonits, F. Caccioli, and I. Kondor, “Replica approach to mean-variance portfolio optimization,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2016, no. 12, Article ID 123404, 2016. View at Publisher · View at Google Scholar · View at Scopus
  25. G. Papp, F. Caccioli, and I. Kondor, “Fluctuation-bias trade-off in portfolio optimization under expected shortfall with l2 regularization,” https://arxiv.org/abs/1602.08297.
  26. G. Sugihara, R. May, H. Ye et al., “Detecting causality in complex ecosystems,” Science, vol. 338, no. 6106, pp. 496–500, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. A. T. Clark, H. Ye, F. Isbell et al., “Spatial convergent cross mapping to detect causal relationships from short time series,” Ecology, vol. 96, no. 5, pp. 1174–1181, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Pearl, Causality, Cambridge University Press, 2009.
  29. J. Massey, Causality, Feedback And Directed Information, Citeseer, 1999.
  30. G. Kramer, Directed information for channels with feedback [PhD thesis], University of Manitoba, Winnipeg, Canada, 1998.
  31. P.-O. Amblard and O. J. Michel, “The relation between Granger causality and directed information theory: a review,” Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, vol. 15, no. 1, pp. 113–143, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus