An empirical Bayes approach to identification of modules in dynamic networks

TL;DR

This paper introduces an empirical Bayes method for identifying specific modules within dynamic networks, leveraging stable spline kernels and an iterative EM algorithm, with extensions for additional measurements and demonstrated effectiveness through numerical experiments.

Contribution

It presents a novel empirical Bayes approach for module identification in dynamic networks with feedback, using stable spline kernels and an iterative EM scheme, including extensions for downstream measurements.

Findings

Effective module identification demonstrated in numerical experiments

Extension of method to include downstream measurements

Iterative scheme based on EM algorithm successfully applied

Abstract

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.