A Bayesian approach to sparse dynamic network identification

Abstract

Modeling and identification for high dimensional (i.e. signals with many components) data sets poses severe challenges to off-the-shelf techniques for system identification. This is particularly so when relatively small data sets, as compared to the number signal components, have to be used. It is often the case that each component of the measured signal can be described in terms of few other measured variables and these dependence can be encoded in a graphical way via so called "Dynamic Bayesian Networks". Finding the interconnection structure as well as the dynamic models can be posed as a system identification problem which involves variables selection. While this variable selection could be performed via standard selection techniques, computational complexity may however be a critical issue, being combinatorial in the number of inputs and outputs. Parametric estimation techniques which result in sparse models have nowadays become very popular and include, among others, the well known Lasso, LAR and their "grouped" versions Group Lasso and Group LAR. In this paper we introduce two new nonparametric techniques which borrow ideas from a recently introduced Kernel estimator called "stable-spline" as well as from sparsity inducing priors which use 1 -type penalties. Numerical experiments regarding estimation of large scale sparse (ARMAX) models show that this technique provides a definite advantage over a group LAR algorithm and state-of-the-art parametric identification techniques based on prediction error minimization.

On optimal input design for networked systems

“…Here we can see the reference as the measurable disturbance. The system can be written in the form (1) by using (2). The control error e c (t) can be written as…”

“…Some recent work on topology identification of networked systems can be found in [18], [19], [23]. If the network is sparsely interconnected, regularization ideas could be applied, see [20] and [2] .…”

Identification of modules in dynamic networks: An empirical Bayes approach

“…Some of the recent papers deal with both the aforementioned problems [4], [5] [1], [6], whereas others are mainly focused on the identification of a single module, see [7] [8], [9], [10], [11]. In particular, [7], [2] study the problem of understanding which of the available output measurements should be used to obtain a consistent estimate of a target module.…”

Identification and Prediction in Dynamic Networks with Unobservable Nodes

“…modeling of a set of internal variables (nodes) that are interconnected through dynamic subsystems (modules), has recently gained in popularity. A common approach to modeling is data-based inference using the system identification methodology, see for instance, Chiuso and Pillonetto (2012), Van den Hof et al (2013), Everitt et al (2014), Gunes et al (2014), and Weerts et al (2015). The data-based modeling field can be divided in two groups depending on the knowledge of the topology, i.e.…”