A causal inference model of spike train interactions in fast response regimes

The idea of estimating synaptic connectivity and strength from parallel spike trains has been entertained since the late 1960s, but the last few years have seen a resurgence in proposed methods. A majority of model-free techniques estimate synaptic coupling via a “separation of timescales” (SOT) principle applied to the cross-correlogram (CCG). That is, a joint distribution is implicitly specified on paired spike trains where it is common to include a fast timescale component (modeling synaptic coupling) and a coarse timescale component (modeling network effects). Such models provide insights into the problem and recent experimental perturbations (e.g., optogenetics) in vivo support SOT. However, simple thought experiments suggest that the CCG is insufficient to isolate causation from correlation when synaptic and network terms have non-trivial dependence structure. By employing concepts from causal inference and nonstationary time series analysis, here we develop a model of spike train coupling that is couched in terms of local (i.e., in time) probabilistic computations, yielding causal inferences in the midst of complex, time-varying dependencies between coupling and network states. The approach combines a nonparametric model of point processes with a causal potential outcomes framework. Under the model, we prove theorems for unbiased point estimation and exact confidence intervals for excitatory and inhibitory coupling. Building on insights from this more rigorous analysis, we proceed to develop a heuristic approach to estimate fractional common cause inputs. Inferences are demonstrated in point process simulations with nonstationarity and dependence structure that maximally conflates correlation and causation.