An empirical Bayes approach to identification of modules in dynamic networks
This work addresses the problem of module identification in dynamic networks for control and systems engineering, but the contribution appears incremental as it extends existing Bayesian approaches with a new iterative scheme.
The paper introduces an empirical Bayes method for identifying a specific module in dynamic networks with feedback loops, using a stable spline kernel and an EM-based iterative scheme. Numerical experiments demonstrate the method's effectiveness.
We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods.