In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements of distributed neuron areas. An effective statistical model for functional connectivity and its changes over time is critical for better understanding the mechanisms of brain and various neurological diseases. To this end, we propose a matrix-log mean model with an additive heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. The heterogeneity of error terms is introduced specifically to capture the curved nature of the manifold. We then propose to use the local scan statistics to detect change patterns in the functional connectivity. Theoretically, we show that our procedure can recover all change points consistently. Simulation studies and an application to the Human Connectome Project lend further support to the proposed methodology.
Understanding the human brain remains the Holy Grail in biomedical science, and arguably in all of the sciences. Our brains represent the most complex systems in the world (and some contend the universe) comprising nearly one hundred billion neurons with septillions of possible connections between them. The structure of these connections engenders an efficient hierarchical system capable of consciousness, as well as complex thoughts, feelings, and behaviors. Brain connectivity and network analyses have exploded over the last decade due to their potential in helping us understand both normal an…
Understanding of normal and pathological brain function requires the identification and localization of functional connections between specialized regions. The availability of high time resolution signals of electric neuronal activity at several regions offers information for quantifying the connections in terms of information flow. When the signals cover the whole cortex, the number of connections is very large, making visualization and interpretation very difficult. We introduce here the singular value decomposition of time-lagged multiple signals, which localizes the senders, hubs, and rece…
Universiti Teknologi Malaysia（马来西亚理工大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of connectivity measure. We propose a deep convolutional neural network (CNN) framework for classification of electroencephalogram (EEG)-derived brain connectome in schizophrenia (SZ). To capture complementary aspects of disrupted connectivity in SZ, we explore combination of vario…
The primary goal of this paper is to develop a method that quantifies how activity in one brain region can explain future activity in another region. Here, we propose the mixed effects spectral vector-autoregressive (ME-SpecVar) model to investigate differences in dynamics of dependence in a brain network between healthy children and those who are diagnosed with ADHD. Specifically, ME-SpecVar model will be used to formally test for significant connectivity structure obtained using filtered EEG signals in delta, theta, alpha, beta, and gamma frequency bands. The suggested model allows one-stage…
Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. For the sake of feasibility, standard models typically reduce dimensionality by modeling covariance among regions of interest (ROI…
Understanding the functional architecture of the brain in terms of networks is becoming increasingly common. In most fMRI applications functional networks are assumed to be stationary, resulting in a single network estimated for the entire time course. However recent results suggest that the connectivity between brain regions is highly non-stationary even at rest. As a result, there is a need for new brain imaging methodologies that comprehensively account for the dynamic (i.e., non-stationary) nature of the fMRI data. In this work we propose the Smooth Incremental Graphical Lasso Estimation (…
Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that causal dependencies arise due to contemporaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that …
Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed networks are treated as matrix-valued responses and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient…
Bayesian Varying-Effects Vector Autoregressive Models for Inference of Brain Connectivity Networks and Covariate Effects in Pediatric Traumatic Brain Injury
This paper concerns the modeling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose a formal test for the weak separability hypothesis, where the asymptotic null distribution of the test statistic is a chi-…
Time-varying networks are fast emerging in a wide range of scientific and business disciplines. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect multi-subject continuous-time stochastic blockmodel that characterizes the time-varying behavior of the network at the population level, meanwhile taking into account individual subject variability. We develop a multi-step optimization procedure for a constrained stochastic blockmodel estimation, and derive the asymptotic property of the estimator. We demonstrate…
Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependences that are often encoded in terms of partial correlations. Such a graph is inferred from matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family o…
Dynamic functional brain connectivity results depend on modeling assumptions: comparing the sliding-window method and the Wishart process for dynamic hypothesis testing
Donders Institute, Radboud University（唐德斯研究所，拉德堡德大学）
Alzheimer's disease (AD) is the most common form of dementia, which causes problems with memory, thinking and behavior. Growing evidence has shown that the brain connectivity network experiences alterations for such a complex disease. Network comparison, also known as differential network analysis, is thus particularly powerful to reveal the disease pathologies and identify clinical biomarkers for medical diagnoses (classification). Data from neurophysiological measurements are multi-dimensional and in matrix-form, which poses major challenges in brain connectivity analysis and medical diagnos…
Dynamic networks have been increasingly used to characterize brain connectivity that varies during resting and task states. In such characterizations, a connectivity network is typically measured at each time point for a subject over a common set of nodes representing brain regions, together with rich subject-level information. A common approach to analyzing such data is an edge-based method that models the connectivity between each pair of nodes separately. However, such approach may have limited performance when the noise level is high and the number of subjects is limited, as it does not ta…
Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on independent samples, there is no readily available solution to test the change of brain network for paired and correlated samples. In this article, we develop a paired test of matrix graphs to infer brain connectivity network when the groups of samples are correlated. The proposed test statistic is both bias corrected and variance corrected, and achieves a small estim…
Epilepsy is a chronic neurological disorder affecting more than 50 million people globally. An epileptic seizure acts like a temporary shock to the neuronal system, disrupting normal electrical activity in the brain. Epilepsy is frequently diagnosed with electroencephalograms (EEGs). Current methods study the time-varying spectra and coherence but do not directly model changes in extreme behavior. Thus, we propose a new approach to characterize brain connectivity based on the joint tail behavior of the EEGs. Our proposed method, the conditional extremal dependence for brain connectivity (Conex…
Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified group of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patt…
Converging evidence indicates that the heterogeneity of cognitive profiles may arise through detectable alternations in brain functions. Particularly, brain functional connectivity, measured under resting and cognitive states, characterizes the unique neuronal interconnections across large-scale brain networks. Despite an unprecedented opportunity to uncover neurobiological subtypes through clustering or subtyping analyses on multi-state functional connectivity, few existing approaches are applicable here to accommodate the network topology and unique biological architecture of functional conn…
The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the structural connectome varies across individuals in relation to their traits, ranging from age and gender to neuropsychiatric outcomes. After applying tractography to dMRI to get white matter fiber bundles, a key question is how to represent the brain connectome to facilitate statistical analyses relating connectomes to traits. The current standard divides the brain …
We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the ex…
Classical scalar-response regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. In medical applications, however, regressors are often in a form of multi-dimensional arrays. For example, one may be interested in using MRI imaging to identify which brain regions are associated with a health outcome. Vectorizing the two-dimensional image arrays is an unsatisfactory approach since it destroys the inherent spatial structure of the images and can be computationally challenging. We present an alternative approach - regularized matrix regressi…
