Statistical perspective on functional and causal neural connectomics: The Time-Aware PC algorithm

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 it 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.Author summary: The functional connectome maps the connections that neurons utilize for information flow in the brain. Such a flow is dynamic and could be expressed as a “cause-and-effect” interaction between neurons. Adding these aspects to the functional connectome corresponds to specifying the direction of connections, i.e., mapping the causal functional connectome. Such a mapping is expected to lead to a more fundamental understanding of brain function and dysfunction. Among statistical frameworks to infer causal relations from observations, directed probabilistic graphical modeling is popular, however, its common formulation is not suitable for neurons since it was developed for variables with independent and identically distributed static samples, whereas neurons are dynamic objects generating time series of activity. In this work, we develop a novel approach for modeling and estimating causal functional connectome by adapting directed probabilistic graphical modeling to the time series scenario. We show its properties of reflecting causal interactions over time and demonstrate its utility in obtaining the causal functional connectome for different datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex. With the article, an open-source Python package is made available. The package provides a full implementation of the methods along with examples.