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High-dimensional multisubject time series transition matrix inference with application to brain connectivity

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Summary

This study introduces a new method for analyzing brain effective connectivity using high-dimensional vector autoregression (VAR) models, addressing measurement error and multiple subjects. The developed procedure accurately infers brain network patterns under challenging conditions.

Keywords:
brain connectivity analysisexpectation-maximizationfunctional magnetic resonance imagingsimultaneous inferencetensor regressionvector autoregression

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Area of Science:

  • Neuroscience
  • Statistics
  • Machine Learning

Background:

  • Effective connectivity analysis reveals directed neural influences, crucial for understanding brain function.
  • Vector autoregression (VAR) models are valuable for this analysis, but existing methods struggle with measurement error, multiple subjects, and transition matrix inference.
  • High-dimensional data in neuroscience presents unique challenges for accurate connectivity modeling.

Purpose of the Study:

  • To develop a robust method for inferring the transition matrix in high-dimensional VAR models with measurement error and multiple subjects.
  • To propose a simultaneous testing procedure that accurately controls false discoveries while maximizing statistical power.
  • To validate the proposed method using both simulated data and real-world functional magnetic resonance imaging (fMRI) data.

Main Methods:

  • A modified expectation-maximization (EM) algorithm was developed to handle measurement error and multiple subjects.
  • A novel test statistic was created using tensor regression on a bias-corrected estimator of lagged auto-covariance.
  • A properly thresholded simultaneous test was implemented for robust inference.

Main Results:

  • The modified EM algorithm demonstrated uniform consistency in its estimations.
  • The proposed testing procedure achieved consistent false discovery control.
  • The statistical power of the test was shown to approach one asymptotically, indicating high efficacy.
  • The method's performance was validated through simulations and application to task-evoked fMRI data.

Conclusions:

  • The developed simultaneous testing procedure offers a powerful and reliable approach for effective connectivity analysis in complex scenarios.
  • This method advances the inference of transition matrices in high-dimensional VAR models, particularly when dealing with measurement error and multiple subjects.
  • The findings have significant implications for understanding brain network dynamics from neuroimaging data.