Estimating sparse Volterra models using group L1-regularization

Sparse Volterra model (sVM) is defined as a Volterra model (VM) that contains only a subset of its all possible model coefficients corresponding to its significant inputs and the existing terms of those inputs. Compared with ordinary VM, sVM is more efficient and interpretable in representing sparsely connected multiple-input systems, e.g., neuronal networks. In this paper, we formulate a rigorous statistical method of estimating sVM based on the group L1-regularization. It allows simultaneous selection and estimation of the significant groups of coefficients of a VM and results in a sVM. Simulation results show that the actual structure of a sVM can be faithfully recovered even with short input-output data. This method can be extended and applied to the identification of the functional connectivity between neurons.