  We address a fundamental problem that is systematically encountered when
modeling complex systems: the limitedness of the information available. In the
case of economic and financial networks, privacy issues severely limit the
information that can be accessed and, as a consequence, the possibility of
correctly estimating the resilience of these systems to events such as
financial shocks, crises and cascade failures. Here we present an innovative
method to reconstruct the structure of such partially-accessible systems, based
on the knowledge of intrinsic node-specific properties and of the number of
connections of only a limited subset of nodes. This information is used to
calibrate an inference procedure based on fundamental concepts derived from
statistical physics, which allows to generate ensembles of directed weighted
networks intended to represent the real system, so that the real network
properties can be estimated with their average values within the ensemble. Here
we test the method both on synthetic and empirical networks, focusing on the
properties that are commonly used to measure systemic risk. Indeed, the method
shows a remarkable robustness with respect to the limitedness of the
information available, thus representing a valuable tool for gaining insights
on privacy-protected economic and financial systems.
