Joint Neural Computation & Machine Learning Thesis Defense

  • Ph.D. Student
  • Joint Ph.D. Program in Neural Computation & Machine Learning
  • Carnegie Mellon University
Thesis Orals

Graphical network modeling of phase coupling in brain activity

Cross-region coordination is reflected in the phase coupling of brain oscillations, which are a strong feature of neural recordings such as local field potentials (LFPs). But the standard method for phase coupling in neuroscience, phase locking value (PLV), is bivariate and thus unable to identify multivariate graphical network structure. In this thesis, I define a cross-region graphical model where the nodes represent phase angle measurements corresponding to different brain regions, and the presence of edges indicate direct pathways (conditional dependence between pairs of nodes). An angle based graphical model has properties analogous to a Gaussian graphical model (a workhorse in machine learning). However, in the Gaussian case a single scalar can describe positive and negative association between two real-valued variables, while for angles, association arises in the form of complex number weights, and we need two complex numbers to describe association between two phase-angle variables. Here, I extend statistical and machine learning methodology from graphical models and hierarchical latent variables to provide a method of making inferences about functional coupling across brain regions from large numbers of oscillatory signals at a fixed frequency, over multiple observations of the same experimental condition.

This thesis has three components. The first is theoretical work on the encoding and transmission of information in the brain (Orellana, et al., J. Neural Computation, 2017). The second develops Torus Graphs (TGs), which are exponential families of multivariate distributions for circular random variables (in press for the Annals of Applied Statistics). The third, extends TGs using latent variables to group measurements within brain regions. In our initial implementation (component two of the thesis), a TG outputs a network graph with as many nodes as the number of electrodes. To capture cross-region coordination, in component three of the thesis, I introduce a latent variable to represent each region and estimate a network graph with as many nodes as the number of brain regions. The utility of this phase coupling methodology is demonstrated on multiple datasets in different memory-recall tasks.

Thesis Committee: 
Rob Kass (Chair)
Valerie Ventura
Max G’Sell
Matt Harrison (Brown University)

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