Torus graphs for multivariate phase coupling analysis
Name
1910.11044.pdf
Description
Submitted version
Size
2.55 MB
Format
Adobe PDF
Checksum (MD5)
8de4b42112381e4d489d475075fe8a99
Author(s)
Klein, Natalie
Orellana, Josue
Brincat, Scott L
Miller, Earl K
Kass, Robert E
Date Issued
2020
Journal
Annals of Applied Statistics
Publisher
Institute of Mathematical Statistics
Citation
Klein, Natalie, Orellana, Josue, Brincat, Scott L, Miller, Earl K and Kass, Robert E. 2020. "Torus graphs for multivariate phase coupling analysis." Annals of Applied Statistics, 14 (2).
Version
Original manuscript
Abstract
© Institute of Mathematical Statistics, 2020. Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.
MIT Department
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/19-AOAS1300
