Non-Gaussian interaction information: Estimation, optimization and diagnostic application of triadic wave resonance

Nonlinear Processes in Geophysics

Volumn 22, Issue 1, 2015, Pages 87-108

  Pires, C A L ^a   Perdigao R A P ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION METHOD; GAUSSIAN METHOD; NUMERICAL MODEL; OPTIMIZATION; PROBABILITY; RESONANCE; WAVE FIELD;

EID: 84961290515     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-22-87-2015     Document Type: Article

References (66)

1. Abramov, R., Majda, A. J., and Kleeman, R.: Information theory and predictability for low-frequency variability, J. Atmos. Sci., 62, 65-87, doi:10.1175/JAS-3373.1, 2005.
2. Almeida, L. B.: MISEP-linear and nonlinear ICA based on mutual information, J. Mach. Learn. Res., 4, 1297-1318, 2003.
3. Almeida, L. B.: Nonlinear Source Separation, Synthesis Lectures on Signal Processing, Morgan and Claypool Publishers, San Rafael, California (USA), 114 pp., doi:10.2200/S00016ED1V01Y200602SPR002, 2006.
4. Bailey, R. A.: Orthogonal partitions for designed experiments, Design Code Cryptogr., 8, 45-77, 1996.
5. Ball, F. K.: Energy transfer between external and internal gravity waves, J. Fluid Mech., 19, 465-478, 1964.
6. Bartello, P.: Geostrophic adjustment and inverse cascades in rotating stratified turbulence, J. Atmos. Sci., 52, 4410-4428, doi:10.1175/1520-0469(1995)052<4410:GAAICI>2.0.CO;2, 1995.
7. Batchelor, G. K.: The Theory of Homogeneous Turbulence, Cambridge University Press, UK, 197 pp., 1953
8. Bellman, R. E., Rand Corporation: Dynamic Programming, Princeton University Press, Princeton, USA, 1957.
9. Bocquet, M., Pires, C. A., and Lin, W.: Beyond Gaussian statistical modeling in geophysical data assimilation, Mon. Weather Rev., 138, 2997-3023, doi:10.1175/2010MWR3164.1, 2010.
10. Comon, P.: Independent component analysis, a new concept?, Signal Process., 36, 287-314, 1994.
11. Cover, T. M. and Thomas, J. A.: Elements of Information Theory, John Wiley&Sons Inc., New York, USA, 1991.
12. DelSole, T.: Predictability and information theory. Part I: Measures of predictability, J. Atmos. Sci., 61, 2425-2440, 2004.
13. Dénes, J. H. and Keedwell, A. D.: Latin Squares and their Applications, Academic Press, New York, London, 547 pp., 1974.
14. Donges, J. F., Zou, Y., Marwan, N., and Kurths, J.: Complex networks in climate dynamics, Eur. Phys. J.-Spec. Top., 174, 157-179, 2009.
15. Evenson, G. and Fario, N.: Solving for the generalized inverse of the Lorenz model, J. Meteorol. Soc. Jpn., 75, 229-243, 1997.
16. Franzke, C., Majda, A. J., and Branstator, G.: The origin of nonlinear signatures of planetary wave dynamics: mean phase space tendencies and contributions from non-Gaussianity, J. Atmos. Sci., 64, 3987-4003, doi:10.1175/2006JAS2221.1, 2007.
17. Friedman, J. H. and Tukey, J.W.: A projection pursuit algorithm for exploratory data analysis, IEEE T. Comput., 23, 881-890, 1975.
18. Gilbert, J. C. and Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms, Math. Program., 45, 407-435, 1989.
19. Globerson, A., Stark, E., Vaadia, E., and Tishby, N.: The minimum information principle and application to neural code analysis, P. Natl. Accd. Sci. USA, 106, 3490-3495, 2009.
20. Granger, C. W. J.: Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37, 424-438, 1969.
21. Hammack, J. L.: Resonant Interactions Among Surface Water Waves, Annu. Rev. Fluid Mech., 25, 55-97, 1993.
22. Hannachi, A. and O'Neill, A.: Atmospheric multiple equilibria and non-Gaussian behaviour in model simulations, Q. J. Roy. Meteor. Soc., 127, 939-958, doi:10.1002/qj.49712757312, 2001.
23. Hannachi, A., Jolliffe, I. T., and Stephenson, D. B.: Empirical orthogonal functions and related techniques in atmospheric science: a review, Int. J. Climatol., 27, 1119-2115, 2007.
24. Hastie, T. and Stuetzle, W.: Principal curves, J. Am. Stat. Assoc., 84, 502-516, 1989.
25. Hastie, T., Tibshirani, R., and Friedman, J.: Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer-Verlag, New York, USA, 2001.
26. Hlinka, J., Hartman, D., Vejmelka, M., Novotná, D., and Palus, M.: Nonlinear dependence and teleconnections in climate data: sources, relevance, nonstationarity, Clim. Dynam., 42, 1873-1886, 2014.
27. Hoffman, D., Raffenetti, R. C., and Ruedenberg, K.: Generalization of Euler angles to N-dimensional orthogonal matrices, J. Math. Phys., 13, 528, doi:10.1063/1.1666011, 1972.
28. Hsieh, W. W., Wu, A., and Shabbar, A.: Nonlinear atmospheric teleconnections, Geophys. Res. Lett., 33, L07714, doi:10.1029/2005GL025471, 2006.
29. Huber, P. J.: Projection pursuit, Ann. Stat., 13, 435-475, doi:10.1214/aos/1176349519, 1985.
30. Hyvärinen, A. and Oja, E.: Independent component analysis: algorithms and application, Neural Netw., 13, 411-430, 2000.
31. Jakulin, A. and Bratko, I.: Quantifying and Visualizing Attribute Interactions: an Approach Based on Entropy, arXiv:cs/0308002v3[cs.AI], 308002, 3 pp., 2004.
32. Jennrich, R. I.: A simple general procedure for orthogonal rotation, Psychometrika, 66, 289-306, 2001.
33. Liang, X. S. and Kleeman, R.: A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping, Physica D, 231, 1-9, 2007.
34. Lorenz, E. N.: Predictability: a problem partly solved, in: Seminar on Predictability, vol. I, ECMWF, Reading, UK, 1-18, available at: http://old.ecmwf.int/publications/library/ecpublications/-pdf/seminar/1995/predictability-lorenz.pdf last access: 23 September 2014), 1995.
35. Lorenz, E. N. and Emanuel, K. A.: Optimal sites for supplementary weather observations: simulation with a small model, J. Atmos. Sci., 55, 399-414, 1998.
36. Majda, A. J., Abramov, R., and Grote, M.: Information Theory and Stochastics for Multiscale Nonlinear Systems, Vol. 25 of CRM Monograph Series, American Mathematical Society, Centre de Recherches Mathématiques, Université de Montréal, 141 pp., 2005.
37. Makarychev, K., Makarychev, Y., Romashchenko, A., and Vereshchagin, N.: A new class of non-Shannon-type inequalities for entropies, Commun. Inform. Syst., 2, 147-166, 2002.
38. McGill, W. J.: Multivariate information transmission, Psychometrika, 19, 97-116, 1954.
39. Monahan, A. H.: Nonlinear principal component analysis: tropical Indo-Pacific sea surface temperature and sea level pressure, J. Climate, 14, 219-233, 2001.
40. Monahan, A. H. and DelSole, T.: Information theoretic measures of dependence, compactness, and non-gaussianity for multivariate probability distributions, Nonlin. Processes Geophys., 16, 57-64, doi:10.5194/npg-16-57-2009, 2009.
41. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA, USA, 1988.
42. Pires, C. A.: Source separation by non-Gaussian dyads of the lowfrequency atmospheric variability, in preparation, 2015.
43. Pires, C. A. and Perdigão, R. A. P.: Non-Gaussianity and asymmetry of the winter monthly precipitation estimation from the NAO, Mon. Weather Rev., 135, 430-448, 2007.
44. Pires, C. A. and Perdigão, R. A. P.: Minimum mutual information and non-Gaussianity through the maximum entropy method: theory and properties, Entropy, 14, 1103-1126, doi:10.3390/e14061103, 2012.
45. Pires, C. A. and Perdigão, R. A. P.: Minimum mutual information and non-Gaussianity through the maximum entropy method: estimation from finite samples, Entropy, 15, 721-752, doi:10.3390/e15030721, 2013.
46. Raffenetti, C. and Ruedenberg, K.: Parametrization of an orthogonal matrix in terms of generalized eulerian angles, Int. J. Quantum Chem., 4, 625-634, doi:10.1002/qua.560040725, 1969.
47. Roulston, M. and Smith, L.: Evaluating probabilistic forecasts using information theory, Mon. Weather Rev., 130, 1653-1660, 2002.
48. Schneidman, E., Still, S., Berry, M. J., and Bialek, W.: Network information and connected correlations, Phys. Rev. Lett, 91, 238701-1-238701-4, 2003.
49. Shannon, C. E.: A mathematical theory of communication, Bell Syst. Tech. J., 27, 379-423, 623-656, 1948.
50. Silverman, B. W.: Density Estimation for Statistics and Data Analysis, Chapman&Hall, London, 176 pp., 1986.
51. Sura, P., Newman, M., Penland, C., and Sardeshmuck, P.: Multiplicative noise and non-Gaussianity: a paradigm for atmospheric regimes?, J. Atmos. Sci., 62, 1391-1406, 2005.
52. Theis, F. J.: Multidimensional independent component analysis using characteristic functions, in: Proceedings of 13th European Signal Processing Conference (EUSIPCO), Antalya, Turkey, 4-8 September, 1692-1695, 2005.
53. Theis, F. J.: Towards a general independent subspace analysis, in: Advances in Neural Information Processing Systems 19, Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems, Vancouver, British Columbia, Canada, 4-7 December 2006.
54. Theis, F. J. and Kawanabe, M.: Uniqueness of non-Gaussian subspace analysis, in: Independent Component Analysis and Blind Signal Separation, edited by: Rosca, J., Erdogmus, D., Príncipe, J. C., and Haykin, S., 6th International Conference, ICA 2006, Charleston, SC, USA, 5-8 March 2006, Lecture Notes in Computer Science, Springer, Berlin, 3889, 2006.
55. Timme, N., Alford, W., Flecker, B., and Beggs, J. M.: Synergy, redundancy, and multivariate information measures: an experimentalist's perspective, J. Comput. Neurosci., 36, 119-140, doi:10.1007/s10827-013-0458-4, 2013.
56. Trendafilov, N. T.: Dynamical system approach to multivariate data analysis, J. Comput. Graph. Stat., 15, 628-650, 2006.
57. Tsujishita, T.: On triple mutual information, Adv. Appl. Math., 16, 269-274, 1995.
58. van den Dool, H. M. and Saha, S.: Empirical orthogonal teleconnections, J. Climate, 18, 1421-1435, doi:10.1175/1520-0442(2000)013<1421:EOT>2.0.CO;2, 2000.
59. van Hulle, M. M.: Edgeworth approximation of multivariate differential entropy, Neural Comput., 17, 1903-1910, 2005.
60. van Leeuwen, P. J.: Nonlinear data assimilation in geosciences: an extremely efficient particle filter, Q. J. Roy. Meteor. Soc., 136, 1991-1999, 2010.
61. Wackernagel, H.: Multivariate Geostatistics-an Introduction with Applications, Springer Verlag, Berlin, Germany, 1995.
62. Wallace, J. M. and Gutzler, D. S.: Teleconnections in the geopotential height field during the Northern Hemisphere winter, Mon. Weather Rev., 109, 784-812, doi:10.1175/1520-0493(1981)109<0784:TITGHF>2.0.CO;2, 1981.
63. Walters-Williams, J. and Li, Y.: Estimation of mutual information: a survey, Lect. Notes Comp. Sci., 5589, 389-396, 2009.
64. Xu, Q.: Measuring information content from observations for data assimilation: relative entropy versus shannon entropy difference, Tellus, 59, 198-209, doi:10.1111/j.1600-0870.2006.00222.x, 2007.
65. Ziman, J. M.: Electrons and Phonons, Clarendon Press, Oxford, 1960.
66. Zupanski, D. A. Y., Hou, S. Q., Zhang, M., Zupanski, C., Kummerow, D., and Cheung, S. H.: Application of information theory in ensemble data assimilation, Q. J. Roy. Meteor. Soc., 133, 1533-1545, 2007.