Signal selection for estimation and identification in networks of dynamic systems: a graphical model approach
For control theorists and network scientists, this work provides a novel graphical model approach to handle partially measured dynamic networks with unknown inputs, though the results are theoretical and lack concrete numerical validation.
This paper addresses estimation and identification in dynamic networks where only some outputs are measured and inputs are inaccessible. Using d-separation from graphical models, it derives optimal sparse estimators and identification methods for networks with loops, creating connections between control theory and machine learning.
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known (or partially known), two associated goals are (i) to derive estimators for nodes of the network which cannot be directly observed or are impractical to measure; and (ii) to quantitatively identify the dynamic relations between nodes. In this article we address both problems in the challenging scenario where only some outputs of the network are being measured and the inputs are not accessible. The approach makes use of the notion of $d$-separation for the graph associated with the network. In the considered class of networks, it is shown that the proposed technique can determine or guide the choice of optimal sparse estimators. The article also derives identification methods that are applicable to cases where loops are present providing a different perspective on the problem of closed-loop identification. The notion of $d$-separation is a central concept in the area of probabilistic graphical models, thus an additional contribution is to create connections between control theory and machine learning techniques.