  The representation of the flow of information between neurons in the brain
based on their activity is termed the causal functional connectome. Such
representation incorporates the dynamic nature of neuronal activity and causal
interactions between them. In contrast to connectome, the causal functional
connectome is not directly observed and needs to be inferred from neural time
series. A popular statistical framework for inferring causal connectivity from
observations is the directed probabilistic graphical modeling. Its common
formulation is not suitable for neural time series since was developed for
variables with independent and identically distributed static samples. In this
work, we propose to model and estimate the causal functional connectivity from
neural time series using a novel approach that adapts directed probabilistic
graphical modeling to the time series scenario. In particular, we develop the
Time-Aware PC (TPC) algorithm for estimating the causal functional
connectivity, which adapts the PC algorithm a state-of-the-art method for
statistical causal inference. We show that the model outcome of TPC has the
properties of reflecting causality of neural interactions such as being
non-parametric, exhibits the directed Markov property in a time-series setting,
and is predictive of the consequence of counterfactual interventions on the
time series. We demonstrate the utility of the methodology to obtain the causal
functional connectome for several datasets including simulations, benchmark
datasets, and recent multi-array electro-physiological recordings from the
mouse visual cortex.
