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Journal of Computational Neuroscience

Erschienen in:

01.02.2011

On directed information theory and Granger causality graphs

verfasst von: Pierre-Olivier Amblard, Olivier J. J. Michel

Erschienen in: Journal of Computational Neuroscience | Ausgabe 1/2011

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Abstract

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.

Vorheriger Artikel Information theory in neuroscience

Nächster Artikel Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

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Achard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. The Journal of Neuroscience, 26(1), 63–72. doi:10.1523/JNEUROSCI.3874-05.2006.CrossRef

Amblard, P. O., & Michel, O. J. J. (2009a). Measuring information flow in networks of stochastic processes. Physical Review E, submitted. ArXiv:cs:IT:/0911.2873v2.

Amblard, P. O., & Michel, O. J. J. (2009b). Sur différentes mesures de dépendance causales entre signaux aléatoires (On different measures of causal dependencies between random signals). In Proc. Gretsi, Dijon, France.

Amblard, P. O., Zozor, S., Michel, O. J. J., & Cuculescu, A. (2008). On the estimation of the entropy using k-th nearest neighbors. In IMA conf. on maths and signal processing (pp. 79–82).

Bach, F., & Jordan, M. I. (2004). Learning graphical models for stationary times series. IEEE Transactions on Signal Processing, 52, 2189–2199.CrossRef

Barnett, L., Barrett, A. B., & Seth, A. K. (2009). Granger causality and transfer entropy are equivalent for Gaussian variables. Physical Review Letters, 103, 23870. arXiv:0910.4514v2.CrossRef

Beirlant, J., Dudewicz, J. E., Gyorfi, L., & Meulen, E. C. V. D. (1997). Nonparametric entropy estimation: An overview. International Journal of Mathematical and Statistical Sciences, 6, 17–39.

Brillinger, D. (1996). Remarks concerning graphical models for time series and point processes. Revista de Econometria, 16, 1–23.

Cover, J., & Thomas, B. (1993). Elements of information theory. New York: Wiley.

Dahlaus, R. (2000). Graphical interaction models for multivariate time series. Metrika, 51, 157–172.CrossRef

Dahlaus, R., & Eichler, M. (2003). Highly structured stochastic systems. In P. Green, N. Hjort, & S. Richardson (Eds.), Chap. Causality and graphical models in time series analysis. Oxford: University Press.

Dahlaus, R., Eichler, M., & Sandkuhler, J. (1997). Identification of synaptic connections in neural ensembles by graphical models. Journal of Neuroscience Methods, 77, 93–107.CrossRef

Eichler, M. (1999). Graphical models in time series analysis. Ph.D. thesis, Ruprecht-Karls-Universit at Heidelberg.

Eichler, M. (2005). A graphical approach for evaluating effective connectivity in neural systems. Philosophical Transactions of the Royal Society of London B, 360, 953–967.CrossRef

Eichler, M. (2006). On the evaluation of information flow in multivariate systems by the directed transfer function. Biological Cybernetics, 94, 469–482.CrossRefPubMed

Frenzel, S., & Pompe, B. (2007). Partial mutual information for coupling analysis of multivariate time series. Physical Review Letters, 99, 204,101.CrossRefPubMed

Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77, 304–313.CrossRef

Good, P. (2005). Permutation, parametric and bootstrap tests of hypotheses. Springer.

Granger, C. W. J. (1980). Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control, 2, 329–352.CrossRef

Granger, C. W. J. (1988). Some recent developments in a concept of causality. Journal of Econometrics, 39, 199–211.CrossRef

Gray, R. M. (1990). Entropy and information theory. New York: Springer.

Gray, R. M., & Kieffer, J. C. (1980). Mutual information rate, distorsion and quantization in metric spaces. IEEE Transactions on Information Theory, 26, 412–422.CrossRef

Hlavackova-Schindlera, K., Palus, M., Vejmelka, M., & Bhattacharya, J. (2007). Causality detection based on information-theoretic approaches in time series analysis. Physics Reports, 441, 1–46.CrossRef

Jirsa, V. K., & McIntosh, A. R. (Eds.) (2007). Handbook of brain connectivity. New York: Springer.

Kaiser, A., & Schreiber, T. (2002). Information transfer in continuous processes. Physica, D 166, 43–62.CrossRef

Kaminski, M., Ding, M., Truccolo, W., & Bressler, S. (2001). Evaluating causal relations in neural systems: Granger causality, directed transfer functions and statistical assessment of significance. Biological Cybernetics, 85, 145–157.CrossRefPubMed

Kramer, G. (1998). Directed information for channels with feedback. Ph.D. thesis, Swiss Federal Institute of Technology Zurich.

Kraskov, A., Stogbauer, H., & Grassberger, P. (2004). Estimating mutual information. Physics Review E, 69, 066,138.CrossRef

Kozachenko, L. F., & Leonenko, N. N. (1987). Sample estimate of the entropy of a random vector. Problems of Information Transmission, 23, 95–101.

Lauritzen, S. (1996). Graphical models. Oxford: Oxford University Press.

Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses (3rd ed.). New York: Springer.

Leonenko, N. N., Pronzato, L., & Savani, V. (2008). A class of Rényi information estimators for multidimensional densities. Annals of Statistics, 36, 2153–2182.CrossRef

Lungarella, M., & Sporns, O. (2006). Mapping information flow in sensorimotor networks. PLOS Computational Biology, 2, 1301–1312.CrossRef

Marko, H. (1973). The bidirectional communication theory—a generalization of information theory. IEEE Transactions on communications, 21(12), 1345–1351.CrossRef

Massey, J. (1990). Causality, feedback and directed information. In Proc. intl. symp. on info. theory and its applications. Waikiki, Hawai, USA.

Michel, O. J. J., & Flandrin, P. (1996). Application of methods based on higher-order statistics for chaotic time series analysis. Signal Processing, 53, 133–148.CrossRef

Palus, M., Komarek, V., Hrncir, Z., & Sterbova, K. (2001). Synchronisation as adjustment of information rates: Detection from bivariate time series. Physics Review E, 046211, 1–6.

Paninski, L. (2003). Estimation of entropy and mutual information. Neural Computation, 15, 1191–1253.CrossRef

Pearl, J. (2000). Causality: Models, reasoning and inference. Cambridge: Cambridge University Press.

Pinsker, M. S. (1964). Information and information stability of random variables. Princeton: Holden Day.

Rissanen, J., & Wax, M. (1987). Measures of mutual and causal dependence between two time series. IEEE Transactions on Information Theory, 33, 598–601.CrossRef

Saito, Y., & Harashima, H. (1981). Recent advances in EEG and EMG data processing. In Chap. Tracking of information within multichannel EEG record-causal analysis in EEG (pp. 133–146). Amsterdam: Elsevier.

Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–465.CrossRefPubMed

Seth, A. K. (2005). Causal connectivity of evolved neural networks during behavior. Network: Computation in Neural Systems, 16, 35–54.CrossRef

Seth, A. K., & Edelman, G. M. (2007). Distinguishing causal interactions in neural populations. Neural Computation, 19, 910–933.CrossRefPubMed

Sporns, O. (2007). Brain connectivity. Scholarpedia, 2(2), 4695. http://www.scholarpedia.org/article/Brain_connectivity.CrossRef

Tatikonda, S., & Mitter, S. (2009). The capacity of channels with feedback. IEEE Transactions on Information Theory, 55, 323–349.CrossRef

Tatikonda, S. C. (2000). Control under communication constraints. Ph.D. thesis, MIT.

Venkataramanan, R., & Pradhan, S. S. (2007). Source coding with feed-forward: Rate-distortion theorems and error exponents for a general source. IEEE transactions on Information Theory, 53, 2154–2179.CrossRef

Victor, J. D. (2002). Binless strategies for estimation of information from neural data. Physics Review E, 66, 051,903-1–15.

Wang, Q., Kulkarni, S., & Verdu, S. (2009). Divergence estimation for multidimensional densities via k-nearest-neighbor distances. IEEE Transactions on Information Theory, 55, 2392–2405.CrossRef

Whittaker, J. (1989). Graphical models in applied multivariate statistics. New York: Wiley.

Titel: On directed information theory and Granger causality graphs
verfasst von: Pierre-Olivier Amblard
Olivier J. J. Michel
Publikationsdatum: 01.02.2011
Verlag: Springer US
Erschienen in: Journal of Computational Neuroscience / Ausgabe 1/2011
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-010-0231-x

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