Information flow among neural networks with Bayesian estimation. (English) Zbl 1134.62366
Summary: Estimating the interaction among neural networks is an interesting issue in neuroscience. Some methods have been proposed to estimate the coupling strength among neural networks; however, few estimations of the coupling direction (information flow) among neural networks have been attempted. It is known that the Bayesian estimator is based on a priori knowledge and the probability of event occurrence. In this paper, a new method is proposed to estimate coupling directions among neural networks with conditional mutual information that is estimated by Bayesian estimation.
First, this method is applied to analyze simulated EEG series generated by a nonlinear lumped-parameter model. In comparison with the conditional mutual information with Shannon entropy, it is found that this method is more successful in estimating the coupling direction, and is insensitive to the length of EEG series. Therefore, this method is suitable to analyze a short time series in practice. Second, we demonstrate how this method can be applied to the analysis of human intracranial epileptic electroencephalogram (EEG) recordings, and to indicate the coupling directions among neural networks. Therefore, this method helps to elucidate the epileptic focus localization.
First, this method is applied to analyze simulated EEG series generated by a nonlinear lumped-parameter model. In comparison with the conditional mutual information with Shannon entropy, it is found that this method is more successful in estimating the coupling direction, and is insensitive to the length of EEG series. Therefore, this method is suitable to analyze a short time series in practice. Second, we demonstrate how this method can be applied to the analysis of human intracranial epileptic electroencephalogram (EEG) recordings, and to indicate the coupling directions among neural networks. Therefore, this method helps to elucidate the epileptic focus localization.
MSC:
| 62M45 | Neural nets and related approaches to inference from stochastic processes |
| 62F15 | Bayesian inference |
| 92C20 | Neural biology |
| 92C55 | Biomedical imaging and signal processing |
| 92C50 | Medical applications (general) |
| 62B10 | Statistical aspects of information-theoretic topics |
References:
| [1] | Rosenblum G M, Pikovsky A. Detecting direction of coupling in interacting oscillators. Phys Rev E, 2001, 64: 045202 |
| [2] | Rosenblum G M. Identification of coupling direction: Application to cardio respiratory interaction. Phys Rev E, 2002, 65: 041909 |
| [3] | Roelfsema P R, Engel A K, Konig P, et al. Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature, 1997, 385: 157–161 · doi:10.1038/385157a0 |
| [4] | Steriade M, McCormick D A. Thalamocortical oscillations in the sleeping and aroused brain. Science, 1993, 262: 679–685 · doi:10.1126/science.8235588 |
| [5] | Miltner W H, Braun C, Arnold M, et al. Coherence of gamma-band EEG activity as a basis for associative learning. Nature, 1999, 397: 434–436 · Zbl 0050.21304 · doi:10.1038/17126 |
| [6] | Rodriguez E, George N, Lachaux J P, et al. Perception’s shadow: Long-distance synchronization of human brain activity. Nature, 1999, 397: 430–433 · doi:10.1038/17120 |
| [7] | Niedermeyer E, Fernando L S. Electroencephalography: Basic Principles, Clinical Applications and Related Fields. Baltimore: Winlliams & Wilkins, 1993. 1097 |
| [8] | Smirnov D A, Andrzejak R G. Detection of weak directional coupling: Phase-dynamics approach versus state-space approach. Phys Rev E, 2005, 71: 036207 |
| [9] | Smirnov D A, Bezruchko B P. Estimation of interaction strength and direction from short and noisy time series. Phys Rev E, 2003, 68: 046209 |
| [10] | Palus M, Stefanovska A. Direction of coupling from phases of interacting oscillators: An information-theoretic approach. Phys Rev E, 2003, 67: 055201 |
| [11] | Yokota Y. An approximate method for Bayesian entropy estimation for a discrete random variable. In: Proceedings of the 26th Annual International Conference of the IEEE EMBS, San Francisco, USA, 2004. 99–102 |
| [12] | Rosenblum G M, Pikovsky A. Phase Synchronization: From Theory to Data Analysis. Handbook of Biological Physics. Vol 4, Neuro-in-formatics. Elsevier Science, 2001. 279–321 |
| [13] | Li X L, Yao X, John R G, et al. Interaction dynamics of neuronal oscillations with wavelet. J Neurosci Meth, 2007, 160(1): 178–185 · doi:10.1016/j.jneumeth.2006.08.006 |
| [14] | Li X L. Temporal structure of neuronal population oscillations with empirical model decomposition. Phys Lett A, 2006, 356(3): 237–241 · Zbl 1160.92336 · doi:10.1016/j.physleta.2006.03.045 |
| [15] | Palus M, Komarek V, Hrncir Z, et al. Synchronization as adjustment of information rates: Detection from bivariate time series. Phys Rev E, 2001, 63: 046211 |
| [16] | Cover T M, Thomas J A. Elements of Information Theory. New York: John Wiley & Sons, 1991 · Zbl 0762.94001 |
| [17] | Lopes da Silva F H, Hoek A, Smith H, et al. Model of brain rythmic activity. Kybernetic, 1974, 15: 27–37 · doi:10.1007/BF00270757 |
| [18] | Jansen B, Rit V G. Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern, 1995, 73(4): 357–366 · Zbl 0827.92010 · doi:10.1007/BF00199471 |
| [19] | Jansen B H, Zouridakis G, Brandt M E. A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern, 1993, 68(3): 275–283 · doi:10.1007/BF00224863 |
| [20] | Wendling F, Bellanger J J, Bartolomei F, et al. Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol Cybern, 2000, 83(4): 367–378 · doi:10.1007/s004220000160 |
| [21] | Li Y, Li X L, Ouyang G X, et al. Strength and direction of phase synchronization of neural networks. In: International Symposium on Neural Networks, Chongqing, China, 2005. 314–319 · Zbl 1082.68655 |
| [22] | Mormann F, Andrzejak R G, Kreuz T. Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilespy patients. Phys Rev E, 2003, 67: 021912 |
| [23] | Li X L, Ouyang G X. Nonlinear similarity analysis for epileptic seizures prediction. Nonlinear Anal-Theor, 2006, 64(8): 1666–1678 · Zbl 1089.92023 · doi:10.1016/j.na.2005.07.014 |
| [24] | Li X L, Kapiris P G, Polygiannakis J, et al. Fractal spectral analysis of pre-epileptic seizures phase: In terms of criticality. J Neural Eng, 2005, 2: 11–15 · doi:10.1088/1741-2560/2/2/002 |
| [25] | Li X L, Ouyang G X, Yao X, et al. Dynamical characteristics of pre-epileptic seizures in rats with recurrence quantification analysis. Phys Lett A, 2004, 333: 164–171 · Zbl 1123.92306 · doi:10.1016/j.physleta.2004.10.028 |
| [26] | Chen Y H, Bressler S L, Ding M Z. Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. J Neurosci Meth, 2006, 150: 228–237 · doi:10.1016/j.jneumeth.2005.06.011 |
| [27] | Schelter B, Winterhalder M, Eichler M, et al. Testing for directed influences among neural signals using partial directed coherence. J Neurosci Meth, 2005, 152: 210–219 · doi:10.1016/j.jneumeth.2005.09.001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
