Matrix-Variate Graphical Models for High-Dimensional Neural Recordings
thesisposted on 2020-10-20, 13:46 authored by Zongge LiuZongge Liu
As large-scale neural recordings become common, many neuroscientific investigations are focused on identifying functional connectivity from spatio-temporal measurements in two or more brain areas. Spatio-temporal data in neural recordings can be viewed as matrix-variate data, where the first dimension is time and the second dimension is space. A matrix-variate Gaussian Graphical model (MGGM) can
be applied to study the conditional dependence between different nodes under the assumption that the overall covariance is the tensor product of the spatial covariance
and temporal covariance. This provides a way to study functional connectivity via the spatial component of the precision matrix. We develop and study penalized
regression methods that enable us to do statistical inference and simultaneous hypothesis testing for multi-session local field potential data. Our approach includes four innovations. First, we provide a simultaneous testing framework for MGGM with a high-dimensional bootstrap technique, which enables us to test the strength of neural connectivity between two brain areas. Second, because estimation of spatial dependence also relies on an accurate estimate for temporal covariance structure, we assume autoregressive temporal dependence and thereby provide estimation of
the temporal precision matrix based on a Cholesky factor decomposition. Third, for spatial precision matrix estimation and inference, we implement group Lasso to jointly estimate multi-graphs and study a new statistic to aggregate information from multiple sessions to improve inference. Finally, using our matrix-variate assumption for high-dimensional data, we develop a novel cross-region dynamic factor analysis model to estimate dynamic neural connectivity across multiple brain regions.
- Doctor of Philosophy (PhD)