This is a collaborated work with Professor Robert E. Kass and Professor Valerie Ventura, in the Department of Statistics & Data Sciences, CMU.
An important outstanding problem in analysis of neural data is to characterize interactions across brain regions from high-dimensional multiple-electrode recordings during a behavioral experiment. Of particular interest are lead-lag effects, indicating possible directional flow of neural information, which are often present only transiently, during short periods of time. We address this problem by harnessing the replication structure of many neurophysiological experiments to estimate latent, non-stationary cross-correlation. Our approach begins with an extension of probabilistic CCA to the time series setting, which provides a model-based interpretation of multiset CCA. Because the covariance matrix describing non-stationary dependence is high-dimensional, we assume sparsity of cross-correlations within a range of possible interesting lead-lag effects. We show that the method can perform well in realistic settings and we apply it to 192 simultaneous local field potential (LFP) recordings from prefrontal cortex (PFC) and visual cortex (area V4) during a visual memory task. We find lead-lag relationships that are highly plausible, being consistent with related results in the literature.