An Instrumental Variable Approach to Functional Network Discovery from Optogenetic Experiments

Understanding how networks of neurons transmit information is crucial to uncovering the underlying mechanisms of brain function. A common measure of communication in neuronal networks is functional connectivity. But, due to the presence of many latent confounding factors in existing experimental paradigms, functional connectivity estimates do not allow a direct interpretation of causal interactions in a network. Here, we aim at addressing this challenge using a quasi-experimental approach, namely Instrumental Variables, in a concurrent optogenetic stimulation of two-photon calcium imaging paradigm. We propose a methodology based on variational inference that allows estimating the spiking activity from blurred and noisy two-photon observations. We then use maximum likelihood estimation to construct a statistical testing framework that allows to distinguish between direct and confounding pairwise effects, by taking a set of random stimulation patterns as the instrumental variables. We demonstrate the utility of our approach using simulated data and compare its performance with existing work. Our results show that the proposed method can achieve high sensitivity and specificity in functional network discovery in presence of confounding effects and using a limited number of stimulation patterns and trials.