Consistent estimation of complete neuronal connectivity in large neuronal populations using sparse “shotgun” neuronal activity sampling

We investigate the properties of the recently proposed “shotgun” sampling approach for the common inputs problem in the functional estimation of neuronal connectivity. We study the asymptotic correctness, the speed of convergence, and the data size requirements of such an approach. We find that the shotgun approach can be expected to allow the inference of the complete connectivity matrix in large neuronal populations under some rather general conditions. However, we find that the posterior error of the shotgun connectivity estimator may grow quickly with the size of the unobserved neuronal populations, the connectivity strength, and the square of the observations’ sparseness. This implies that the shotgun connectivity estimation will require significant amounts of neuronal activity data whenever the number of neurons in the observed populations is small. We present a numerical approach for solving the shotgun estimation problem in general settings and use it to demonstrate the shotgun connectivity inference in simulated synfire and weakly coupled cortical neuronal networks.