4,704 research outputs found
Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models
Recent studies on analyzing dynamic brain connectivity rely on sliding-window
analysis or time-varying coefficient models which are unable to capture both
smooth and abrupt changes simultaneously. Emerging evidence suggests
state-related changes in brain connectivity where dependence structure
alternates between a finite number of latent states or regimes. Another
challenge is inference of full-brain networks with large number of nodes. We
employ a Markov-switching dynamic factor model in which the state-driven
time-varying connectivity regimes of high-dimensional fMRI data are
characterized by lower-dimensional common latent factors, following a
regime-switching process. It enables a reliable, data-adaptive estimation of
change-points of connectivity regimes and the massive dependencies associated
with each regime. We consider the switching VAR to quantity the dynamic
effective connectivity. We propose a three-step estimation procedure: (1)
extracting the factors using principal component analysis (PCA) and (2)
identifying dynamic connectivity states using the factor-based switching vector
autoregressive (VAR) models in a state-space formulation using Kalman filter
and expectation-maximization (EM) algorithm, and (3) constructing the
high-dimensional connectivity metrics for each state based on subspace
estimates. Simulation results show that our proposed estimator outperforms the
K-means clustering of time-windowed coefficients, providing more accurate
estimation of regime dynamics and connectivity metrics in high-dimensional
settings. Applications to analyzing resting-state fMRI data identify dynamic
changes in brain states during rest, and reveal distinct directed connectivity
patterns and modular organization in resting-state networks across different
states.Comment: 21 page
Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches
In the past two decades, functional Magnetic Resonance Imaging has been used
to relate neuronal network activity to cognitive processing and behaviour.
Recently this approach has been augmented by algorithms that allow us to infer
causal links between component populations of neuronal networks. Multiple
inference procedures have been proposed to approach this research question but
so far, each method has limitations when it comes to establishing whole-brain
connectivity patterns. In this work, we discuss eight ways to infer causality
in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality,
Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and
Transfer Entropy. We finish with formulating some recommendations for the
future directions in this area
Information Flow in Computational Systems
We develop a theoretical framework for defining and identifying flows of
information in computational systems. Here, a computational system is assumed
to be a directed graph, with "clocked" nodes that send transmissions to each
other along the edges of the graph at discrete points in time. We are
interested in a definition that captures the dynamic flow of information about
a specific message, and which guarantees an unbroken "information path" between
appropriately defined inputs and outputs in the directed graph. Prior measures,
including those based on Granger Causality and Directed Information, fail to
provide clear assumptions and guarantees about when they correctly reflect
information flow about a message. We take a systematic approach---iterating
through candidate definitions and counterexamples---to arrive at a definition
for information flow that is based on conditional mutual information, and which
satisfies desirable properties, including the existence of information paths.
Finally, we describe how information flow might be detected in a noiseless
setting, and provide an algorithm to identify information paths on the
time-unrolled graph of a computational system.Comment: Significantly revised version which was accepted for publication at
the IEEE Transactions on Information Theor
Doctor of Philosophy
dissertationFunctional magnetic resonance imaging (fMRI) measures the change of oxygen consumption level in the blood vessels of the human brain, hence indirectly detecting the neuronal activity. Resting-state fMRI (rs-fMRI) is used to identify the intrinsic functional patterns of the brain when there is no external stimulus. Accurate estimation of intrinsic activity is important for understanding the functional organization and dynamics of the brain, as well as differences in the functional networks of patients with mental disorders. This dissertation aims to robustly estimate the functional connectivities and networks of the human brain using rs-fMRI data of multiple subjects. We use Markov random field (MRF), an undirected graphical model to represent the statistical dependency among the functional network variables. Graphical models describe multivariate probability distributions that can be factorized and represented by a graph. By defining the nodes and the edges along with their weights according to our assumptions, we build soft constraints into the graph structure as prior information. We explore various approximate optimization methods including variational Bayesian, graph cuts, and Markov chain Monte Carlo sampling (MCMC). We develop the random field models to solve three related problems. In the first problem, the goal is to detect the pairwise connectivity between gray matter voxels in a rs-fMRI dataset of the single subject. We define a six-dimensional graph to represent our prior information that two voxels are more likely to be connected if their spatial neighbors are connected. The posterior mean of the connectivity variables are estimated by variational inference, also known as mean field theory in statistical physics. The proposed method proves to outperform the standard spatial smoothing and is able to detect finer patterns of brain activity. Our second work aims to identify multiple functional systems. We define a Potts model, a special case of MRF, on the network label variables, and define von Mises-Fisher distribution on the normalized fMRI signal. The inference is significantly more difficult than the binary classification in the previous problem. We use MCMC to draw samples from the posterior distribution of network labels. In the third application, we extend the graphical model to the multiple subject scenario. By building a graph including the network labels of both a group map and the subject label maps, we define a hierarchical model that has richer structure than the flat single-subject model, and captures the shared patterns as well as the variation among the subjects. All three solutions are data-driven Bayesian methods, which estimate model parameters from the data. The experiments show that by the regularization of MRF, the functional network maps we estimate are more accurate and more consistent across multiple sessions
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