  Understanding the relation between cortical neuronal network structure and
neuronal activity is a fundamental unresolved question in neuroscience, with
implications to our understanding of the mechanism by which neuronal networks
evolve over time, spontaneously or under stimulation. It requires a method for
inferring the structure and composition of a network from neuronal activities.
Tracking the evolution of networks and their changing functionality will
provide invaluable insight into the occurrence of plasticity and the underlying
learning process. We devise a probabilistic method for inferring the effective
network structure by integrating techniques from Bayesian statistics,
statistical physics and principled machine learning. The method and resulting
algorithm allow one to infer the effective network structure, identify the
excitatory and inhibitory nature of its constituents, and predict neuronal
spiking activities by employing the inferred structure. We validate the method
and algorithm's performance using synthetic data, spontaneous activity of an in
silico emulator and realistic in vitro neuronal networks of modular and
homogeneous connectivity, demonstrating excellent structure inference and
activity prediction. We also show that our method outperforms commonly used
existing methods for inferring neuronal network structure. Inferring the
evolving effective structure of neuronal networks will provide new insight into
the learning process due to stimulation in general and will facilitate the
development of neuron-based circuits with computing capabilities.
