Thesis (Ph. D.)--University of Rochester. Department of Electrical Engineering, 2019.
The existence of networks is ubiquitous in natural as well as man-made systems.
Identifying the underlying network structure of components of a complex system, especially
from simultaneously observed signals, is an actively growing area of research.
One of the biggest challenges encountered with network modeling from time-series
data is that we rarely know the underlying network structure governing interactions
amongst the signals. Thus, the task to be accomplished for such problems is that the
network modeling technique should be well-equipped to characterize different types
of interactions. Interactions (i) may be casual in nature, (ii) may have nonlinear
dependencies, (iii) may take place with different components interacting directly or
indirectly with others (iv) may be part of a large or small system. Hence, network
modeling approaches should be formulated keeping these different characteristics of
interaction in mind. To this end, this work presents three approaches that can detect
causal relationships, in systems regardless of size. These approaches are first tested
and validated on various simulations with a known underlying network structure of
interactions. Subsequently, they are evaluated on real brain activity data recorded
using functional magnetic resonance imaging (fMRI).
Studies on how the brain is connected and how different regions communicate is
a growing and evolving field, as improvements in fMRI technology call for improved
analysis techniques. One of the three investigated approaches that is nonlinear uses
local models to extract the underlying network structure from fMRI data for both
simulated and real data. Such an approach uses state space reconstruction to estimate
causality. We also develop two extensions to Granger causality analysis that can
determine network graphs for large systems. These approaches are not susceptible to
falsely capturing indirect connections since they are multivariate. We first develop
a linear multivariate Granger causality analysis approach called large-scale Granger
causality (lsGC). Subsequently, we develop large-scale nonlinear Granger causality
(lsNGC), which is an extension of lsGC as it accounts for nonlinear dependencies.
Methods currently adopted in fMRI literature are either too simplistic and unable
to capture the various types of interactions or are too complex and cannot be extended
to large systems. With the aforementioned approaches, we demonstrate that
the three investigated network modeling techniques can characterize complex interactions
without being severely impacted by network size and limited observations.
These methods can potentially replace traditional correlation-based approaches used
to estimate the network structure in fMRI. Additionally, they can also be used to aid
model-driven approaches that require a pre-specified network structure. Furthermore,
the promising results on experimental fMRI data suggest that these approaches may
aid in identifying imaging-derived biomarkers that can assist clinicians in monitoring
disease progression and response to therapeutic intervention for patients with a wide
range of neurological and psychiatric disorders.