On Identification of Dynamical Structure Functions: A Sparse Bayesian Learning Approach.

This paper considers the identification of linear time-invariant networks, also known as dynamic structure functions. Assuming identifiability of the network addressed in previous work, this paper presents an identification method that infers both the Boolean structure of the network and the transfer functions between nodes. The identification is performed directly from data and without any prior knowledge of the system, including its order. The method is to formulate the identification as a linear regression problem together with penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). We then propose a novel scheme that combines sparse Bayesian and sparse group Bayesian to efficiently solve the problem. The method and the developed toolbox can now be used to infer networks from a wide range of fields, including systems biology applications such as signalling and genetic regulatory networks.