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Modeling High-Dimensional Multichannel Brain Signals

Author

Listed:
  • Lechuan Hu

    (University of California)

  • Norbert J. Fortin

    (University of California)

  • Hernando Ombao

    (University of California
    King Abdullah University of Science and Technology (KAUST))

Abstract

Our goal is to model and measure functional and effective (directional) connectivity in multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The difficulties from analyzing these data mainly come from two aspects: first, there are major statistical and computational challenges for modeling and analyzing high-dimensional multichannel brain signals; second, there is no set of universally agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO $$+$$ + LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). Then we employ some measures of connectivity but put an emphasis on partial directed coherence (PDC) which can capture the directional connectivity between channels. PDC is a frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the network. The proposed modeling approach provided key insights into potential functional relationships among simultaneously recorded sites during performance of a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types.

Suggested Citation

  • Lechuan Hu & Norbert J. Fortin & Hernando Ombao, 2019. "Modeling High-Dimensional Multichannel Brain Signals," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 91-126, April.
  • Handle: RePEc:spr:stabio:v:11:y:2019:i:1:d:10.1007_s12561-017-9210-3
    DOI: 10.1007/s12561-017-9210-3
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    References listed on IDEAS

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    1. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    3. Ivanov Ventzislav & Kilian Lutz, 2005. "A Practitioner's Guide to Lag Order Selection For VAR Impulse Response Analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-36, March.
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    Cited by:

    1. Hu, Lechuan & Guindani, Michele & Fortin, Norbert J. & Ombao, Hernando, 2020. "A hierarchical bayesian model for differential connectivity in multi-trial brain signals," Econometrics and Statistics, Elsevier, vol. 15(C), pages 117-135.
    2. Dallakyan, Aramayis & Kim, Rakheon & Pourahmadi, Mohsen, 2022. "Time series graphical lasso and sparse VAR estimation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

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