Discovery of Functional Predictivity across Brain Regions from Local Field Potentials
Neural recordings from high-density microelectrode arrays yield high-dimensional time-series observations, simultaneously recorded from multiple brain regions, with good spatial and temporal resolution. A careful study of such time-series covariance structure can uncover functional associations between the regions, and in particular, lead-lag relationships could indicate possible directional flows of neural information. Because such relationships in an alert animal’s brain are observed transiently, we use repeated trials to estimate the non-stationary covariance structure. In this thesis work, we develop methods for estimating non-stationary lead-lag relationships among high-dimensional time series.
The first approach is to treat high-dimensional time-series recordings as matrix-variate observations and model them by matrix-variate Gaussian graphical models. In these models, two covariance matrices describe spatial association between the LFP channels and autocorrelation across time, respectively. We discover cross-regional connectivity using statistical inference on the spatial covariance graph estimate. We proved the theoretical validity of the proposed bootstrap test, based on high-dimensional central limit theorems. We showed that the proposed method increases statistical power by incorporating the shared covariance structures in multiple recording sessions. We also demonstrate the efficacy of the new method through both simulated datasets and multi-session LFP recordings from the same experiment as in LaDyS.
Another approach is based on extensions of probabilistic canonical correlation analysis (pCCA) to the time-series setting. Starting with recordings from only two brain regions, the model assumes that all of the time series within a given region are driven by the same latent univariate time series; the resulting latent bivariate time series then defines the time-varying cross-region dependence we seek to identify. By leaving the correlation matrix unspecified instead of assuming a parametric structure for the cross-dependence, the model provides a model-based interpretation of multiset CCA. These generalizations come at a cost: we now have a high-dimensional time series problem within each brain region, involving a high-dimensional covariance structure. We solved these high-dimensional problems by imposing sparsity of the dominant effects within a range of possible interesting lead-lag effects and developed Latent Dynamic Analysis via Sparse Banded Graphs (LaDynS).
We also developed and studied inferential procedures to decide time epochs of significant cross-region association from the LaDynS estimate. In particular, an autoregressive model, based on the LaDynS estimate, enables statistical inferences of cross-regional association in terms of Granger causality. LaDynS performed well in simulations designed to mimic real-data situations. We also applied it to 192 simultaneous local field potential (LFP) recordings from the prefrontal cortex (PFC) and visual cortex (area V4) during a visual memory task. We found lead-lag relationships that are highly plausible and consistent with related results in the literature.
Furthermore, we developed an improved method, Latent Dynamic Factor Analysis of High-dimensional Timeseries (LDFA-H), by incorporating the two previous methods. LDFA-H uses the LaDynS latent factor models to describe cross-regional connectivity, while imposing a spatio-temporal matrix-variate graphical model on autocorrelations within brain areas. This hierarchical structure allows LDFA-H to provide better estimates than LaDynS and other known methods, even in the presence of high noise.
Last, we revisit covariance structure in LFP recordings in context of the oscillatory nature of the data mode. We considered phase and amplitude together using the complex normal distribution, for which the distinction between covariance and pseudo-covariance is important. This provides a new characterization of standard oscillatory correlation measures, based on conditional distributions of phase given amplitude. We defined a complex Gaussian latent variable model for evaluating the strength of associations across multiple brain areas and applied it to data involving multivariate LFP time series that exhibit pronounced oscillations.
- Statistics and Data Science
- Doctor of Philosophy (PhD)