  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. A leading theory,
based on a considerable body of research, is that oscillations represent
coordinated activity across populations of neurons. We sought to quantify
time-varying covariation of oscillatory amplitudes across two brain regions,
during a memory task, based on neural potentials recorded from 96 electrodes in
each region. We extended probabilistic Canonical Correlation Analysis (CCA) to
the time series setting, which provides a new interpretation of multiset CCA
based on cross-correlation of latent time series. Because the latent time
series covariance matrix is high-dimensional, we assumed sparsity of partial
correlations within a range of possible interesting time series lead-lag
effects to derive procedures for estimation and inference. We found the
resulting methodology to perform well in realistic settings, and we applied it
to data recorded from prefrontal cortex and visual area V4 to produce results
that are highly plausible based on existing literature.
