A mathematical framework for inferring connectivity in probabilistic neuronal networks.

We describe an approach for determining causal connections among nodes of a probabilistic network even when many nodes remain unobservable. The unobservable nodes introduce ambiguity into the estimate of the causal structure. However, in some experimental contexts, such as those commonly used in neuroscience, this ambiguity is present even without unobservable nodes. The analysis is presented in terms of a point process model of a neuronal network, though the approach can be generalized to other contexts. The analysis depends on the existence of a model that captures the relationship between nodal activity and a set of measurable external variables. The mathematical framework is sufficiently general to allow a large class of such models. The results are modestly robust to deviations from model assumptions, though additional validation methods are needed to assess the success of the results.