Forecasting the evolution of nonlinear and nonstationary systems using recurrence-based local Gaussian process models

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Bukkapatnam, Satish T S ^a   Cheng, Changqing ^a  

^a Oklahoma State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN; CLASSICAL SYSTEMS; COMPLEX PHYSICAL SYSTEMS; COMPUTATIONAL SPEED; GAUSSIAN PROCESS; GAUSSIAN PROCESS MODELS; GAUSSIAN PROCESSES; HEART-RATE; HIGHLY NONLINEAR; INDUCED NOISE; INDUSTRIAL OPERATIONS; LOOK-AHEAD; LORENZ SYSTEM; NON-PARAMETRIC; NON-PARAMETRIC MODEL; NON-STATIONARITIES; NON-STATIONARY DYNAMICS; NONSTATIONARY SYSTEMS; PARTITION SYSTEMS; PERFORMANCE FORECASTING; PIECEWISE AFFINES; PREDICTION ACCURACY; PREDICTION MODEL; REAL-WORLD; TOPOLOGICAL PROPERTIES; UNDERLYING DYNAMICS; UNDERLYING SYSTEMS;

FORECASTING; GAUSSIAN NOISE (ELECTRONIC); MATHEMATICAL MODELS; MODELS; MONTE CARLO METHODS; NEURAL NETWORKS; TOPOLOGY;

GAUSSIAN DISTRIBUTION;

EID: 78651346497     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.056206     Document Type: Article

References (46)

1. J. M. Wang, D. J. Fleet, and A. Hertzmann, IEEE Trans. Pattern Anal. Mach. Intell. 30, 283 (2008). 10.1109/TPAMI.2007.1167
2. T. Lang, C. Plagemann, and W. Burgard, Robotics (Science and Systems, Atlanta, GA, 2007).
3. N.-T. Duy and J. Peters, in Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE Service Center, Piscataway, NJ 2008).
4. J. Gao, J. Appl. Probab. 41, 467 (2004). 10.1239/jap/1082999079
5. C. C. Strelioff and A. W. Hübler, Phys. Rev. Lett. 96, 044101 (2006). 10.1103/PhysRevLett.96.044101
6. D. S. Broomhead and G. P. King, Physica D 20, 217 (1986). 10.1016/0167-2789(86)90031-X
7. C. M. Danforth and J. A. Yorke, Phys. Rev. Lett. 96, 144102 (2006). 10.1103/PhysRevLett.96.144102
8. M. C. Casdagli, Physica D 108, 12 (1997). 10.1016/S0167-2789(97)82003-9
9. J. B. Gao, Y. Cao, L. Gu, J. G. Harris, and J. C. Principe, Phys. Lett. A 317, 64 (2003). 10.1016/j.physleta.2003.08.018
10. N. Marwan, M. Carmen Romano, M. Thiel, and J. Kurths, Phys. Rep. 438, 237 (2007). 10.1016/j.physrep.2006.11.001
11. R. Yulmetyev, P. Hänggi, and F. Gafarov, Nonlinear Phenom. Complex Syst. (Dordrecht, Neth.) 5, 129 (2002).
12. C. E. Rasmussen and C. K. I. Williams, Gaussian Process for Machine Learning (MIT Press, Cambridge, MA, 2006).
13. M. Gibbs, Ph.D. dissertation, University of Cambridge, 1997.
14. R. P. Adams and O. Stegle, in Proceedings of the 25th International Conference on Machine Learning, Helsinki, Finland (ACM, New York, 2008).
15. J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, Europhys. Lett. 4, 973 (1987). 10.1209/0295-5075/4/9/004
16. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, England, 1995).
17. T. P. Minka, Ph.D. dissertation, Massachusetts Institute of Technology, 2001.
18. C. J. Paciorek and M. J. Schervish, in Proceedings of the Conference on Neural Information Processing Systems (NIPS), 2004 (MIT Press, Cambridge, MA, 2004).
19. C. E. Rasmussen and Z. Ghahramani, in The 2001 Neural Information Processing Systems (NIPS) Conference (MIT Press, Cambridge, MA, 2004).
20. E. Snelson and Z. Ghahramani, in Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, San Juan, Puerto Rico (MIT Press, Cambridge, MA, 2007).
21. J. Quinonero-Candela and C. E. Rasmussen, J. Mach. Learn. Res. 6, 1939 (2005).
22. G. Gregorcic and G. Lightbody, IEEE Trans. Neural Netw. 18, 1404 (2007). 10.1109/TNN.2007.895825
23. E. Meeds and S. Osindero, Advances in Neural Information Processing Systems (MIT Press, Cambridge, MA, 2006).
24. J. Q. Shi, R. Murray-Smith, and D. M. Titterington, Int. J. Adapt. Control Signal Process. 17, 149 (2003). 10.1002/acs.744
25. V. Tresp, in The 2001 Neural Information Processing Systems (NIPS) Conference (MIT Press, Cambridge, MA, 2001).
26. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986). 10.1103/PhysRevA.33.1134
27. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992). 10.1103/PhysRevA.45.3403
28. F. Takens, Lecture Notes in Mathematics (Springer, Berlin, 1981), Vol. 898.
29. G. F. V. Amaral, C. Letellier, and L. A. Aguirre, Chaos 16, 013115 (2006). 10.1063/1.2149527
30. H. Yang, Ph.D. dissertation, Oklahoma State University, 2009.
31. R. E. Walpole and R. H. Myers, Probability & Statistics for Engineers & Scientists (Macmillan, New York, 1989).
32. S. Calinon, F. Guenter, and A. Billard, IEEE Trans. Syst., Man, Cybern., Part B: Cybern. 37, 286 (2007). 10.1109/TSMCB.2006.886952
33. F. Orderud, in Proceedings of Scandinavian Conference on Simulation and Modeling (Tapir Academic Press, Trondhem, 2005).
34. H. Min, X. Jianhui, X. Shiguo, and Y. Fu-Liang, IEEE Trans. Signal Process. 52, 3409 (2004). 10.1109/TSP.2004.837418
35. D. Gencaga, A. Ertuzun, and E. E. Kuruoglu, Digit. Signal Process. 18, 465 (2008). 10.1016/j.dsp.2007.04.011
36. C. Letellier, Chaos 17, 023104 (2007). 10.1063/1.2645725
37. M. Shen and F. Shen, in IEEE Signal Processing Workshop on Higher-Order Statistics, edited by, C. Banff,, (IEEE Signal Processing Society, Baniff, Alberta, Canada, 1997).
38. E. Ghysels and D. R. Osborn, The Econometric Analysis of Seasonal Time Series (Cambridge University Press, Cambridge, England, 2001).
39. J. Xu, L. Duran, and P. Pibarot, IEEE Trans. Biomed. Eng. 47, 1328 (2000). 10.1109/10.871405
40. Z. Chen, P. C. Ivanov, K. Hu, and H. E. Stanley, Phys. Rev. E 65, 041107 (2002). 10.1103/PhysRevE.65.041107
41. A. Subbu and A. Ray, Appl. Phys. Lett. 92, 084107 (2008). 10.1063/1.2883958
42. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, England, 2001). 10.1017/CBO9780511755743
43. J. M. Nichols, M. D. Todd, M. Seaver, and L. N. Virgin, Phys. Rev. E 67, 016209 (2003). 10.1103/PhysRevE.67.016209
44. S. T. S. Bukkapatnam, J. M. Nichols, M. Seaver, S. T. Trickey, and M. Hunter, Struct. Health Monit. 4, 247 (2005). 10.1177/1475921705055246
45. A. Braga, A. C. Carvalho, T. Ludermir, M. d. Almeida, and E. Lacerda, Modeling and Forecasting Financial Data: Techniques of Nonlinear Dynamics (Kluwer Academic Publishers, Dordrecht, 2002).
46. R. C. Sharpley and V. Vatchev, Constructive Approx. 24, 17 (2006). 10.1007/s00365-005-0603-z