Identification of modules in dynamic networks: An empirical Bayes approach

Abstract

Abstract-We address the problem of identifying a specific module in a dynamic network, 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 ExpectationMaximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method.

Learning sparse linear dynamic networks in a hyper-parameter free setting

“…Various approaches have been considered in the estimation of topology and dynamics in network systems. Frequencydomain methods have been proposed for identification of networks (Materassi and Innocenti, 2010;Shahrampour and Preciado, 2015) Module-based analysis and characterization of dynamic networks and conditions on identificability under diverse system conditions have been studied (Everitt et al, 2016;Gevers and Bazanella, 2015;Hendrickx et al, 2019;Materassi and Salapaka, 2016;Van den Hof et al, 2013;Van den Hof et al, 2012). Regularized regression approaches which leverage on model sparsity have been explored (Bolstad et al, 2011;Jahandari and Materassi, 2018;Materassi et al, 2013;Yuan and Lin, 2006).…”

“…Regularized regression approaches which leverage on model sparsity have been explored (Bolstad et al, 2011;Jahandari and Materassi, 2018;Materassi et al, 2013;Yuan and Lin, 2006). By modelling the transfer function parameters as structured random variables, Bayesian approaches have been also developed (Chiuso and Pillonetto, 2012;Everitt et al, 2016;Everitt et al, 2018;Shi et al, 2019;Zorzi and Chiuso, 2015). Among these, the works of Chiuso and Pillonetto (2012) and Shi et al (2019) are the closest in context to our contribution.…”

Identification of virtual plants using bayesian networks based on parametric L-system

“…Probability theory deals with the data directly, while graph theory relates directly with the desired representation. The Bayesian networks method is a good method for learning process that is based on data training that uses conditional probability as the basis [14]. Bayesian networks consist of two main parts:…”

An empirical Bayes approach to identification of modules in dynamic networks

“…The methods proposed in this paper are close in spirit to some recently proposed kernel-based techniques for blind system identification and Hammerstein system identification . A part of this paper has previously been presented in Everitt, Bottegal, Rojas and Hjalmarsson (2016). More specifically, the case where only the sensors directly measuring the input and the output of the target module are used in the identification process where partly covered in Everitt, Bottegal, Rojas and Hjalmarsson (2016), whereas, the method where more sensors spread in the network are used in the identification of the target module is completely novel.…”