An Information-Theoretic Measure of Multiscale Causality for Spike-Field Activity

Simultaneous recordings of spikes and fields could enable analyses of functional connectivity in the brain at multiple spatiotemporal scales. However, these analyses require developing novel methods to assess causality between binary-valued spikes and continuous-valued fields, which have fundamentally different statistical profiles and time-scales. Thus classical measures of causality cannot be directly applied in multiscale networks. We develop a novel parametric method to assess causality for multiscale spike-field activities by computing directed information. Directed information is an information theoretic measure of causality but is in general hard to estimate. Our method estimates the causality in two steps. First, we construct point process generalized linear models (GLM) for each neuron's spiking activity to estimate its firing rate using the history of both spikes and fields and compute the directed information to spike nodes from any node. Second, we construct regression models for fields using the history of the estimated firing rates and the history of fields, and then compute the directed information to each field node from any node. In both steps, we estimate model parameters using maximum likelihood and devise statistical tests to assess the significance of the causality. Using simulated data from basic three-node structures and a ten-node network, we show that our method can asymptotically identify the true causality. This method could help uncover functional connectivity in the brain at multiple spatiotemporal scales.