Causation entropy from symbolic representations of dynamical systems

Chaos

Volumn 25, Issue 4, 2015, Pages

  Cafaro, Carlo ^a   Lord, Warren M ^a   Sun, Jie ^a   Bollt, Erik M ^a  

^a CLARKSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84927127466     PISSN: 10541500     EISSN: 10897682     Source Type: Journal    
DOI: 10.1063/1.4916902     Document Type: Article

References (60)

1. A. Lesne, "Chaos in biology," Riv. Biologia-Biology Forum 99, 413-428 (2006).
2. Q. Gao, X. Duan, and H. Chen, "Evaluation of effective connectivity of motor areas during motor imagery and execution using conditional Granger causality," NeuroImage 54, 1280 (2011).10.1016/j.neuroimage.2010.08.071
3. R. Vicente, M. Wibral, M. Lindner, and G. Pipa, "Transfer entropy-a model-free measure of effective connectivity for the neurosciences," J. Comput. Neurosci. 30, 45 (2011).10.1007/s10827-010-0262-3
4. T. Schreiber, "Measuring information transfer," Phys. Rev. Lett. 85, 461 (2000).10.1103/PhysRevLett.85.461
5. K. J. Rothman and S. Greenland, "Causation and causal inference in epidemiology," Am. J. Public Health 95, S144 (2005).10.2105/AJPH.2004.059204
6. K. Hlavackova-Schindler, M. Palus, M. Vejmelka, and J. Bhattacharya, "Causality detection based on information-theoretic approaches in time series analysis," Phys. Rep. 441, 1 (2007).10.1016/j.physrep.2006.12.004
7. S. Frenzel and B. Pompe, "Partial mutual information for coupling analysis of multivariate time series," Phys. Rev. Lett. 99, 204101 (2007).10.1103/PhysRevLett.99.204101
8. S. Guo, A. K., Seth, K. M. Kendrick, C. Zhou, and J. Feng, "Partial Granger causality-Eliminating exogenous inputs and latent variables," J. Neurosci. Methods 172, 79 (2008).10.1016/j.jneumeth.2008.04.011
9. J. J. Heckman, "Econometric causality," Int. Stat. Rev. 76, 1 (2008).10.1111/j.1751-5823.2007.00024.x
10. A. B. Barrett, L. Barnett, and A. K. Seth, "Multivariate granger causality and generalized variance," Phys. Rev. E 81, 041907 (2010).10.1103/PhysRevE.81.041907
11. T. S. Cubitt, J. Eisert, and M. W. Wolf, "Extracting dynamical equations from experimental data is NP hard," Phys. Rev. Lett. 108, 120503 (2012).10.1103/PhysRevLett.108.120503
12. J. Runge, J. Heitzig, V. Petoukhov, and J. Kurths, "Escaping the curse of dimensionality in estimating multivariate transfer entropy," Phys. Rev. Lett. 108, 258701 (2012).10.1103/PhysRevLett.108.258701
13. J. Runge, J. Heitzig, N. Marwan, and J. Kurths, "Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy," Phys. Rev. E 86, 061121 (2012).10.1103/PhysRevE.86.061121
14. D. Marinazzo, M. Pellicoro, and S. Stramaglia, "Causal information approach to partial conditioning in multivariate data sets," Comput. Math. Methods Med. 2012, 303601.10.1155/2012/303601
15. J. Sun and E. M. Bollt, "Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings," Physica D 267, 49 (2014).10.1016/j.physd.2013.07.001
16. J. Sun, D. Taylor, and E. M. Bollt, "Causal network inference by optimal causation entropy," SIAM J. Appl. Dyn. Syst. 14, 73-106 (2015).10.1137/140956166
17. J. Sun, C. Cafaro, and E. M. Bollt, "Identifying coupling structure in complex systems through the optimal causation entropy principle," Entropy 16, 3416 (2014).10.3390/e16063416
18. A. Porta, L. Faes, V. Bari, A. Marchi, T. Bassani et al., "Effect of age on complexity and causality of the cardiovascular control: Comparison between model-based and model-free approaches," PLoS One 9, e89463 (2014).10.1371/journal.pone.0089463
19. P. Spirtes, C. N. Glymour, and R. Scheines, Causation, Prediction, and Search (MIT Press, 2000).
20. G. A. Darbellay and I. Vajda, "Estimation of the information by an adaptive partitioning of the observation space," IEEE Trans. Inform. Theory 45, 1315 (1999).10.1109/18.761290
21. C. Bandt and B. Pompe, "Permutation entropy: A natural complexity measure for time series," Phys. Rev. Lett. 88, 174102 (2002).10.1103/PhysRevLett.88.174102
22. J. M. Amigo, M. B. Kennel, and L. Kocarev, "The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems," Physica D 210, 77 (2005).10.1016/j.physd.2005.07.006
23. M. Staniek and K. Lehnertz, "Symbolic transfer entropy," Phys. Rev. Lett. 100, 158101 (2008).10.1103/PhysRevLett.100.158101
24. D. Kugiumtzis, "Transfer entropy on rank vectors," J. Nonlinear Syst. Appl. 3, 73 (2012).
25. T. Haruna and K. Nakajima, "Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes," Eur. Phys. J. B 86, 230 (2013).10.1140/epjb/e2013-30721-4
26. K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer-Verlag New York, Inc., 1996).
27. E. M. Bollt and N. Santitissadeekorn, Applied and Computational Measurable Dynamics (Society for Industrial and Applied Mathematics, 2013).
28. A. Boyarsky and P. Gora, Laws of Chaos: Invariant Measures and Dynamical Systems in one Dimension. Probability and Its Applications (Birkhauser Boston, Boston, MA, 1997).
29. D. A. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding (Cambridge University Press, Cambridge, UK, 1995).
30. D. Lind, "Multi-dimensional symbolic dynamics," Proc. Symp. Appl. Math. 60, 61 (2004).10.1090/psapm/060/2078846
31. B. Kitchens, Symbolic Dynamics: One-Sided, Two-Sided, and Countable State Markov Shifts (Springer, 1998).
32. E. A. Robinson, Jr., "Symbolic dynamics and tiling in ?d," Proc. Symp. Appl. Math. 60, 81 (2004).10.1090/psapm/060/2078847
33. E. M. Bollt, T. Stanford, Y.-C. Lai, and K. Zyczkowski, "Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series," Phys. Rev. Lett. 85, 3524 (2000).10.1103/PhysRevLett.85.3524
34. E. M. Bollt, T. Stanford, Y.-C. Lai, and K. Zyczkowski, "What symbolic dynamics do we get with a misplaced partition? On the validity of threshold crossing analysis of chaotic time-series," Physica D 154, 259 (2001).10.1016/S0167-2789(01)00242-1
35. D. J. Rudolph, Fundamentals of Measurable Dynamics, Ergodic Theory and Lebesgue Spaces (Clarendon Press, Oxford, 1990).
36. E. M. Bollt and J. Skufca, Markov Partitions, Encyclopedia of Nonlinear Science, edited by A. Scot (Routledge, New York, 2005).
37. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems (Birkhauser Boston, 2009).
38. H. Teramoto and T. Komatsuzaki, "How does a choice of Markov partition affect the resultant symbolic dynamics?," Chaos 20, 037113 (2010).10.1063/1.3491097
39. O. Pfante, E. Olbrich, N. Bertschinger, N. Ay, and J. Jost, "Closure measures for coarse-graining of the tent map," Chaos 24, 013136 (2014).10.1063/1.4869075
40. R. G. Gallager, Stochastic Processes, Theory for Applications (Cambridge University Press, Cambridge, UK, 2013).
41. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379 (1948).10.1002/j.1538-7305.1948.tb01338.x
42. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (John Wiley & Son, Inc., Hoboken, New Jersey, USA, 2006).
43. M. Ragwitz and H. Kantz, "Markov models from data by simple nonlinear time series predictors in delay embedding spaces," Phys. Rev. E 65, 056201 (2002).10.1103/PhysRevE.65.056201
44. M. Papapetrou and D. Kugiumtzis, "Markov chain order estimation with conditional mutual information," Physica A 392, 1593 (2013).10.1016/j.physa.2012.12.017
45. S. D. Pethel and D. W. Hahs, "Exact significance test for Markov order," Physica D 269, 42 (2014).10.1016/j.physd.2013.11.014
46. J. Pearl, Causality: Models, Reasoning, and Inference, 2nd ed. (Cambridge University Press, Cambridge, UK, 2009).
47. N. Draper and H. Smith, Applied Regression Analysis, 2nd ed. (John Wiley & Sons, Inc., New York, 1981).
48. P. Grassberger, "Finite sample corrections to entropy and dimension estimates," Phys. Lett. A 128, 369 (1988).10.1016/0375-9601(88)90193-4
49. P. Grassberger, "Entropy estimates from insufficient samplings," preprint arXiv:physics/0307138 (2008).
50. J. P. Crutchfield and N. H. Packard, "Symbolic dynamics of one-dimensional maps: entropies, finite precision, and noise," Int. J. Theor. Phys. 21, 433 (1982).10.1007/BF02650178
51. P. Grassberger and H. Kantz, "Generating partitions for the dissipative Henon map," Phys. Lett. A113, 235 (1985).10.1016/0375-9601(85)90016-7
52. Y.-C. Lai, E. M. Bollt, and C. Grebogi, "Communicating with chaos using two-dimensional symbolic dynamics," Phys. Lett. A 255, 75 (1999).10.1016/S0375-9601(99)00175-9
53. R. L. Davidchack, Y.-C. Lai, E. M. Bollt, and M. Dhamala, "Estimating generating partitions of chaotic systems by unstable periodic orbits," Phys. Rev. E 61, 1353 (2000).10.1103/PhysRevE.61.1353
54. B. Pompe and J. Runge, "Momentary information transfer as a coupling measure of time series," Phys. Rev. E 83, 051122 (2011).10.1103/PhysRevE.83.051122
55. A. Kraskov, H. Stogbauer, and P. Grassberger, "Estimating mutual information," Phys. Rev. E 69, 066138 (2004).10.1103/PhysRevE.69.066138
56. M. Vejmelka and M. Palus, "Inferring the directionality of coupling with conditional mutual information," Phys. Rev. E 77, 026214 (2008).10.1103/PhysRevE.77.026214
57. I. Vlachos and D. Kugiumtzis, "Nonuniform state-space reconstruction and coupling detection," Phys. Rev. E 82, 016207 (2010).10.1103/PhysRevE.82.016207
58. A. Porta, P. Castiglioni, V. Bari, T. Bassani, A. Marchi, A. Cividjian, L. Quintin, and M. Di Rienzo, "K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control," Physiol. Meas. 34, 17 (2013).10.1088/0967-3334/34/1/17
59. C. Cafaro, S. Capozziello, and S. Mancini, "On relativistic quantum information properties of entangled wave vectors of massive fermions," Int. J. Theor. Phys. 51, 2313 (2012).10.1007/s10773-012-1111-0
60. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, 1995).