  Dynamic network reconstruction has been shown to be challenging due to the
requirements on sparse network structures and network identifiability. The
direct parametric method (e.g., using ARX models) requires a large amount of
parameters in model selection. Amongst the parametric models, only a restricted
class can easily be used to address network sparsity without rendering the
optimization problem intractable. To overcome these problems, this paper
presents a state-space-based method, which significantly reduces the number of
unknown parameters in model selection. Furthermore, we avoid various
difficulties arising in gradient computation by using the Expectation
Minimization (EM) algorithm instead. To enhance network sparsity, the prior
distribution is constructed by using the Sparse Bayesian Learning (SBL)
approach in the M-step. To solve the SBL problem, another EM algorithm is
embedded, where we impose conditions on network identifiability in each
iteration. In a sum, this paper provides a solution to reconstruct dynamic
networks that avoids the difficulties inherent to gradient computation and
simplifies the model selection.
