Robert E. Kass

Thursday 25th April 2019

Time:1.00pm

Ground Floor Seminar Room

25 Howland Street, London, W1T 4JG

Torus Graphs for Multivariate Phase Coupling Analysis

Interdependence among multiple brain regions is of great interest, and a leading theory is that communication across areas may be facilitated by neural oscillations. One way to establish association of multiple oscillating signals is by showing their phases to be correlated (across repeated measurements). We describe an example in which 24 recordings have been made simultaneously from 4 regions of the brain, repeatedly, during a memory task (data are from the lab of Earl Miller at MIT). To analyze such multivariate angular data, it would be possible to check all relevant pairs of signals using an angular analogue of correlation, known as Phase Locking Value (PLV). While useful, PLV is unable to reveal multivariate dependencies: PLV is analogous to correlation, but with multiple angles it is desirable to have an analogue of partial correlation. We have developed a natural analogue, and this produces a functional connectivity graph. Our approach derives the natural analogue to Gaussian graphical models, which we call torus graphs, because angles lie on the circle and the product of circles is a torus. We show that torus graphs have nice properties and, in the data, find phase relationships that PLV obscures. Interestingly, dependence in torus graphs can be quite different than in Gaussian graphs: in the bivariate Gaussian case, a single scalar, correlation, can describe both positive and negative association; in a 2-dimensional torus graph a complete description of association requires 2 complex numbers. The torus graph framework should be useful whenever it is of interest to examine functional connectivity among multiple oscillating brain areas.