  This paper begins with considering the identification of sparse linear
time-invariant networks described by multivariable ARX models. Such models
possess relatively simple structure thus used as a benchmark to promote further
research. With identifiability of the network guaranteed, this paper presents
an identification method that infers both the Boolean structure of the network
and the internal dynamics between nodes. Identification is performed directly
from data without any prior knowledge of the system, including its order. The
proposed method solves the identification problem using Maximum a posteriori
estimation (MAP) but with inseparable penalties for complexity, both in terms
of element (order of nonzero connections) and group sparsity (network
topology). Such an approach is widely applied in Compressive Sensing (CS) and
known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that
combines sparse Bayesian and group sparse Bayesian to efficiently solve the
problem. The resulted algorithm has a similar form of the standard Sparse Group
Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted
SGL. The method and the developed toolbox can be applied to infer networks from
a wide range of fields, including systems biology applications such as
signaling and genetic regulatory networks.
