Uncovering Network Architecture Using an Exact Statistical Input-Output Relation of a Neuron Model
Using observed neuronal activity, we try to unveil hidden microcircuits. A key requirement is the knowledge of statistical input-output relation of single neurons in vivo. We use a recent exact solution of spike-timing for leaky integrate-and-fire neurons under noisy inputs balanced near threshold, and construct a framework that links synaptic type/strength, and spiking nonlinearity, with statistics of neuronal activity. The framework explains structured higher-order interactions of neurons receiving common inputs under different architectures. Comparing models prediction with an empirical dataset of monkey V1 neurons, we find that excitatory inputs to pairs explain the observed sparse activity characterized by negative triple-wise interactions, ruling out the intuitive shared inhibition. We show that the strong interactions are in general the signature of excitatory rather than inhibitory inputs whenever spontaneous activity is low. Finally, we present a guide map that can be used to reveal the hidden motifs underlying observed interactions found in empirical data.