Shrinkage estimation of high-dimensional vector autoregressions for effective connectivity in fMRI

Hui-Ru Tan, Chee-Ming Ting, Sh-Hussain Salleh, I. Kamarulafizam, A. M. Noor

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We consider the challenge of estimating effective brain connectivity network with a large number of nodes from fMRI data. This involves estimation of a very-high dimensional vector autoregressive (VAR) models commonly used to identify directed brain networks. The conventional least-squares (LS) estimator is not longer consistent when applied on the high-dimensional fMRI data compared to sample size due to large number of fitted parameters, and thus produces unreliable estimates of the brain connectivity. In this paper, we propose an well-conditioned large-dimensional VAR estimator based on shrinkage approach, by incorporating a Ledoit-Wolf (LW) shrinkage-based estimator of the Gramian matrix in the LS-based linear regression fitting of VAR. This allows better-conditioned and invertible Gramian matrix estimate which is an important ingredient in generating a reliable LS estimator, when the data dimension is larger than the sample size. Simulation results show significant superiority of the proposed LW-shrinkage-VAR estimator over the conventional LS estimator under the high-dimensional settings. Application to real resting-state fMRI dataset shows the capability of the proposed method in identifying resting-state brain connectivity networks, with directionality of connections and interesting modular structure, which potentially provide useful insights to neuroscience studies of human brain connectome.

Original languageEnglish
Title of host publicationIECBES 2016 - IEEE-EMBS Conference on Biomedical Engineering and Sciences
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781467377911
Publication statusPublished - 2016
Externally publishedYes
EventIEEE-EMBS International Conference on Biomedical Engineering and Sciences (IECBES) 2016 - Kuala Lumpur, Malaysia
Duration: 4 Dec 20168 Dec 2016 (Proceedings)


ConferenceIEEE-EMBS International Conference on Biomedical Engineering and Sciences (IECBES) 2016
Abbreviated titleIECBES 2016
CityKuala Lumpur
Internet address


  • brain connectivity
  • fMRI
  • high-dimensional
  • shrinkage
  • VAR

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