Beyond Linear Dynamic Functional Connectivity: A Vine Copula Change Point Model

Abstract

To estimate dynamic functional connectivity for functional magnetic resonance imaging (fMRI) data, two approaches have dominated: sliding window and change point methods. While computationally feasible, the sliding window approach has several limitations. In addition, the existing change point methods assume a Gaussian distribution for and linear dependencies between the fMRI time series. In this work, we introduce a new methodology called Vine Copula Change Point (VCCP) to estimate change points in the functional connectivity network structure between brain regions. It uses vine copulas, various state-of-the-art segmentation methods to identify multiple change points, and a likelihood ratio test or the stationary bootstrap for inference. The vine copulas allow for various forms of dependence between brain regions including tail, symmetric and asymmetric dependence, which has not been explored before in the dynamic analysis of neuroimaging data. We apply VCCP to various simulation datasets and to two fMRI datasets: a reading task and an anxiety inducing experiment. In particular, for the former dataset, we illustrate the complexity of textual changes during the reading of Chapter 9 in Harry Potter and the Sorcerer’s Stone and find that change points across subjects are related to changes in more than one type of textual attributes. Further, the graphs created by the vine copulas indicate the importance of working beyond Gaussianity and linear dependence. Finally, the R package vccp implementing the methodology from the article is available from CRAN. Supplementary Materials for this article are available online.

Keyword:

• Computational statistics
• Graphical models
• Networks: fMRI
• Time-varying networks

Supplementary Materials

R Code and Data: The supplemental files for this article include files containing R code and data for reproducing the simulation study and some of the fMRI results in the article. Please see the README.txt file for specific details on how to run the code.

Supplementary Materials: The supplemental files for this article also include the following: (i) definitions of Kendall’s $\tau$ and copula formulas, (ii) additional information on the Harry Potter fMRI dataset, (iii) additional information on the anxiety fMRI dataset, (iv) figures explaining the setup of the non-Gaussian simulations in the article (v) descriptions of the setup of the multivariate normal (MVN) and the vector autoregression (VAR) simulations, (vi) additional results from the Harry Potter and the anxiety fMRI datasets, and (vii) simulation results from the MVN and the VAR simulations

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Funding

Additional information

Funding

X. Xiong was supported by a China Council Scholarship and the work of I. Cribben was supported by the Natural Sciences and Engineering Research Council (Canada) grant RGPIN-2018-06638 and the Xerox Faculty Fellowship, Alberta School of Business.