2 research outputs found
A Hierarchical Graphical Model for Big Inverse Covariance Estimation with an Application to fMRI
Brain networks has attracted the interests of many neuroscientists. From
functional MRI (fMRI) data, statistical tools have been developed to recover
brain networks. However, the dimensionality of whole-brain fMRI, usually in
hundreds of thousands, challenges the applicability of these methods. We
develop a hierarchical graphical model (HGM) to remediate this difficulty. This
model introduces a hidden layer of networks based on sparse Gaussian graphical
models, and the observed data are sampled from individual network nodes. In
fMRI, the network layer models the underlying signals of different brain
functional units, and how these units directly interact with each other. The
introduction of this hierarchical structure not only provides a formal and
interpretable approach, but also enables efficient computation for inferring
big networks with hundreds of thousands of nodes. Based on the conditional
convexity of our formulation, we develop an alternating update algorithm to
compute the HGM model parameters simultaneously. The effectiveness of this
approach is demonstrated on simulated data and a real dataset from a stop/go
fMRI experiment.Comment: An R package of the proposed method will be publicly available on
CRAN. This paper has been presented orally at Yale University on Feburary 18,
2014, and at the Eastern North American Region Meeting of the International
Biometric Society on March 18, 201
Quantifying the strength of structural connectivity underlying functional brain networks
In recent years, there has been strong interest in neuroscience studies to
investigate brain organization through networks of brain regions that
demonstrate strong functional connectivity (FC). These networks are extracted
from observed fMRI using data-driven analytic methods such as independent
component analysis (ICA). A notable limitation of these FC methods is that they
do not provide any information on the underlying structural connectivity (SC),
which is believed to serve as the basis for interregional interactions in brain
activity. We propose a new statistical measure of the strength of SC (sSC)
underlying FC networks obtained from data-driven methods. The sSC measure is
developed using information from diffusion tensor imaging (DTI) data, and can
be applied to compare the strength of SC across different FC networks.
Furthermore, we propose a reliability index for data-driven FC networks to
measure the reproducibility of the networks through re-sampling the observed
data. To perform statistical inference such as hypothesis testing on the sSC,
we develop a formal variance estimator of sSC based a spatial semivariogram
model with a novel distance metric. We demonstrate the performance of the sSC
measure and its estimation and inference methods with simulation studies. For
real data analysis, we apply our methods to a multimodal imaging study with
resting-state fMRI and DTI data from 20 healthy controls and 20 subjects with
major depressive disorder. Results show that well-known resting state networks
all demonstrate higher SC within the network as compared to the average
structural connections across the brain. We also found that sSC is positively
associated with the reliability index, indicating that the FC networks that
have stronger underlying SC are more reproducible across samples.Comment: 25 pages, 4 figure