The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi

Cardiorespiratory fitness as a predictor of effective connectivity in the default mode network

Previous work has linked the onset and progression of Alzheimer’s Disease (AD) to changes in the Default Mode Network (DMN), including greater atrophy within the hippocampus (HC) as well as diminished functional connectivity and effective connectivity between anatomical DMN structures. Animal models have described the HC as a primary region of interest in studying the effects of exercise on adult neurogenesis and memory performance. Human studies have demonstrated that aerobic exercise leads to greater cardiorespiratory fitness and improved functional connectivity in the DMN for healthy adults. The goal of this study is to go beyond the predictions of human and animal studies to investigate how cardiorespiratory fitness may be used to estimate effective connectivity between the HC and the other DMN structures for young adults using resting state fMRI. Due to the data driven nature of this study, no hypothesis has been formulated. To investigate, data from 25 sedentary young adults was analyzed. Data included a resting state fMRI procedure and a cardiorespiratory fitness test, each taken from part of a larger ongoing clinical trial in the Brain Plasticity and Neuroimaging (BPN) Lab at Boston University (BU). We utilized group independent component analysis (GICA) to identify the regions that define the DMN and Conditional Granger Causality Analysis (CGCA) to determine effective connectivity between these regions. GICA indicated 9 structural regions in the DMN, consistent with previous work. This resulted in 72 possible instances of effective connectivity. The difference of causal influence between regions was calculated for each pair of DMN regions for CGCA, resulting in 36 possible instances of causal connectivity. Linear regression models were created to analyze the effect of cardiorespiratory fitness on effective connectivity between DMN regions and found 11 linear models which exhibited a significant (p > 0.05) relationship. Eight of eleven models involved the left or right hippocampus, showing that greater cardiorespiratory fitness is correlated with changes effective connectivity between the HC and the PCC, MPFC, or LTC. These results provide proof of concept that cardiorespiratory fitness in young adults is associated with changes DMN effective connectivity, particularly involving the hippocampus. This adds to the literature suggesting extended aerobic exercise, which is known to increase cardiorespiratory fitness and has been shown to increase the volume of the HC in older adults, may be neuroprotective of the HC across the lifespan. Further investigation is required to explore how effective connectivity in the DMN changes following an aerobic exercise intervention

NOVEL STATISTICAL METHODS FOR MODELING BRAIN AND OTHER DENSE, WEIGHTED NETWORKS

Advances in brain imaging have led to the generation of new kinds of datasets. The novel structures of these datasets necessitate development of new modeling paradigms for analysis better suited to this domain. This work is composed of different projects that propose novel statistical methods for analyzing brain data and other kinds of networks, which are described below. The first project studies the problem of testing for the equality of autocovariances of two independent high-dimensional time series. Tests based on the suprema or sums of suitable averages across the dimensions are adapted from the available literature. Another test based on principal component analysis (PCA) is introduced and studied in theory. An extension is also considered to the setting of testing for the equality of autocovariances of two populations, having multiple individual high-dimensional series from the two populations. The proposed methodologies are assessed on simulated data, with the performance of the introduced PCA testing being superior overall. An application using fMRI data from individuals experiencing two different emotional states is provided. These tests are further developed into a method for detecting change points within a single session. A different notion of detecting a change is explored in the second project. Alzheimer's disease (AD) is a multi-factor neurodegenerative disease that selectively affects certain regions of the brain while other areas remain unaffected. The underlying mechanisms of this selectivity, however, are still largely elusive. A novel longitudinal network analysis method is proposed to address this challenge by employing sparse logistic regression to identify frequency-specific oscillation patterns which contribute to the selective network vulnerability for patients at risk of advancing to the more severe stage of dementia. The statistical method is fit and applied to more than 100 longitudinal brain networks, and validated on synthetic data. A set of critical connectome pathways are identified that exhibit strong association to the progression of AD. The third project attempts to create a mechanism for generating networks similar to those observed in brain scans. Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. A new framework for generating and estimating dense, weighted networks with different connectivity patterns across different groups is introduced. The proposed model relies on a particular class of functions which map individual node characteristics to the edges connecting those nodes. By leveraging the estimation techniques, a bootstrap methodology for generating new networks on the same set of vertices is also developed, which may be useful in circumstances where it is costly to collect multiple data sets. Performance of these methods are analyzed in theory, simulations, and real data. An extension of the previous project to partially observed bipartite networks is also discussed. The application of interest is recommender systems, where nodes of users and items share weighted edges. In this construct, the weight of each edge reflects the affinity between a user and item. In general, most users have not interacted with most items, so those edges are unobserved, but the underlying affinity may still be estimated. Tools developed for analyzing dense weighted networks are updated to match this setting, and estimation results are compared to those achieved by graph neural networks at different levels of missingness.Doctor of Philosoph

Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.Comment: 27 pages, 10 figure

Pyrcca: Regularized Kernel Canonical Correlation Analysis in Python and Its Applications to Neuroimaging

Canonical correlation analysis (CCA) is a valuable method for interpreting cross-covariance across related datasets of different dimensionality. There are many potential applications of CCA to neuroimaging data analysis. For instance, CCA can be used for finding functional similarities across fMRI datasets collected from multiple subjects without resampling individual datasets to a template anatomy. In this paper, we introduce Pyrcca, an open-source Python module for executing CCA between two or more datasets. Pyrcca can be used to implement CCA with or without regularization, and with or without linear or a Gaussian kernelization of the datasets. We demonstrate an application of CCA implemented with Pyrcca to neuroimaging data analysis. We use CCA to find a data-driven set of functional response patterns that are similar across individual subjects in a natural movie experiment. We then demonstrate how this set of response patterns discovered by CCA can be used to accurately predict subject responses to novel natural movie stimuli