  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.
