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Using time-delayed mutual information to discover and interpret temporal correlation structure in complex populations
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1.
1. C. Komalapriya, M. Thiel, M. C. Ramano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217 (2008).
http://dx.doi.org/10.1103/PhysRevE.78.066217
2.
2. J. C. Sprott, Chaos and Time-series Analysis (Oxford University Press, New York, 2003).
3.
3. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, 2nd ed. (Cambridge University Press, UK, 2003).
4.
4. W. Hogan and M. Wagner, J. Am. Med. Inform Assoc. 5, 342 (1997).
http://dx.doi.org/10.1136/jamia.1997.0040342
5.
5. J. van der Lei, Methods Inf. Med. 30, 79 (1991).
6.
6. H. Sagreiya and R. B. Altman, J. Biomed. Inf. 43, 747 (2010).
http://dx.doi.org/10.1016/j.jbi.2010.03.014
7.
7. J. M. Higgins and L. Mahadevan, Proc. Natl. Acad. Soc. U.S.A. 107, 20587 (2010).
http://dx.doi.org/10.1073/pnas.1012747107
8.
8. E. Shudo, R. M. Ribeiro, and A. S. Perelson, J. Viral Hepat. 15, 357 (2008).
http://dx.doi.org/10.1111/j.1365-2893.2007.00954.x
9.
9. M. S. Turner, Phys. Today 62, 8 (2009).
http://dx.doi.org/10.1063/1.3226778
10.
10. J. D. Scargle, Astrophys. J. 263, 835 (1982).
http://dx.doi.org/10.1086/160554
11.
11. S. Baisch and G. H. R. Bokelmann, Comput. Geosci. 25, 739 (1999).
http://dx.doi.org/10.1016/S0098-3004(99)00026-6
12.
12. M. Schulta and K. Stattegger, Comput. Geosci. 23, 929 (1997).
http://dx.doi.org/10.1016/S0098-3004(97)00087-3
13.
13. A. W. C. Liew, J. Xian, S. Wu, D. Smith, and H. Yan, BMC Bioinf. 8, 137 (2007).
http://dx.doi.org/10.1186/1471-2105-8-137
14.
14. L. Wasserman, All of Statistics: A Concise Course in Statistical Inference, (Springer, New York, 2004).
15.
15. M. Loéve, Probability Theory I (Springer-Verlag, 1977).
16.
16. A. G. Gray and A. W. Moore, “Very fast multivariate kernel density estimation using via computational geometry,” in Joint Stat. Meeting (August 4th, 2003).
17.
17. Y.-I. Moon, B. Rajagopalan, and U. Lall, Phys. Rev. E 52, 2318 (1995).
http://dx.doi.org/10.1103/PhysRevE.52.2318
18.
18. R. J. May, G. C. Dandy, H. R. Maier, and T. M. K. G. Fernando, “Critical values of a kernel density-based mutual information estimator,” in International Joint Conference on Neural Networks (IEEE, Vancouver, BC, 2006).
19.
19. D. J. Albers and G. Hripcsak, Estimation of time-delayed mutual information from sparsely sampled sources, e-print arXiv:1110.1615, 2011.
20.
20. R. L. Wheeden and A. Zygmund, “Measure and integral,” in Monographs and Textbooks in Pure and Applied Mathematics (Marcel Dekker, Inc., New York, 1977), Vol. 43.
21.
21. G. P. Basharin, Theor. Probab. Appl. 4, 333 (1959).
http://dx.doi.org/10.1137/1104033
22.
22. M. S. Roulston, Physica D 125, 285 (1999).
http://dx.doi.org/10.1016/S0167-2789(98)00269-3
23.
23. J. Graxzyk and G. Światek, Ann. Math. 146, 1 (1997).
http://dx.doi.org/10.2307/2951831
24.
24. M. Jakobson, Commun. Math. Phys. 81, 39 (1981).
http://dx.doi.org/10.1007/BF01941800
25.
25. D. J. Albers and G. Hripcsak, Phys. Lett. A 374, 1159 (2010).
http://dx.doi.org/10.1016/j.physleta.2009.12.067
26.
26. D. J. Albers and G. Hripcsak, Using population scale EHR data to understand and test human physiological dynamics, e-print arXiv:1110.3317, 2011.
27.
27. It may seem odd to normalize indices, but this just keeps the domain of between zero and one.
28.
28. To see the variation in the PDF estimates due to small sample sizes, observe the PDF estimates for different sets of uniform random numbers with small cardinality.
29.
29. Note, the L1 difference is not technically a distance function or a metric because it does not satisfy the triangle inequality.
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/content/aip/journal/chaos/22/1/10.1063/1.3675621
2012-01-24
2014-11-24

Abstract

This paper addresses how to calculate and interpret the time-delayed mutual information (TDMI) for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle used for this analysis is a comparison between the time-delayed mutual information averaged over the population and the time-delayed mutual information of an aggregated population (here, aggregation implies the population is conjoined before any statistical estimates are implemented). Through the use of information theoretic tools, a sequence of practically implementable calculations are detailed that allow for the average and aggregate time-delayed mutual information to be interpreted. Moreover, these calculations can also be used to understand the degree of homo or heterogeneity present in the population. To demonstrate that the proposed methods can be used in nearly any situation, the methods are applied and demonstrated on the time series of glucose measurements from two different subpopulations of individuals from the Columbia University Medical Center electronic health record repository, revealing a picture of the composition of the population as well as physiological features.

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Scitation: Using time-delayed mutual information to discover and interpret temporal correlation structure in complex populations
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/1/10.1063/1.3675621
10.1063/1.3675621
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