Estimating Multiscale Direct Causality Graphs in Neural Spike-Field Networks

Neural representations span various spatiotemporal scales of brain activity, from the spiking activity of single neurons to field activity measuring large-scale networks. The simultaneous analyses of spikes and fields to uncover causal interactions in multiscale networks could help understand neural mechanisms. However, assessing causality within spike-field networks is challenging as spikes are binary-valued with a fast time-scale while fields are continuous-valued with slower time-scales. Current causality measures are largely not applicable to mixed discrete-continuous network activity. Here, in this paper, we develop a novel multiscale causality estimation algorithm for spike-field networks. We construct a likelihood function comprised of point process models for spikes and linear Gaussian models for fields. For spikes, firing rates are modeled as a function of the history of both field signals and binary spike events within the network. For fields, to make their linear models consistent with biophysical findings, we use the history of field signals and the history of the latent log-firing rates of neurons as predictors. To resolve the challenge of estimating the network model parameters in the presence of latent firing rates, we develop a sequential maximum-likelihood parameter estimation procedure that extends to large networks. Once models are estimated, we compute directed information as our measure of multiscale causality and devise two statistical tests to assess its significance. Using extensive simulations, we show that the algorithm can accurately reconstruct the true causality graphs of random spike-field networks. Moreover, the algorithm is robust to the number of connections, connection strengths, or exact topology of the network. This multiscale causality estimation algorithm has important implications for studying neural mechanisms and for future neurotechnology design.