  This paper develops an active sensing method to estimate the relative weight
(or trust) agents place on their neighbors' information in a social network.
The model used for the regression is based on the steady state equation in the
linear DeGroot model under the influence of stubborn agents, i.e., agents whose
opinions are not influenced by their neighbors. This method can be viewed as a
\emph{social RADAR}, where the stubborn agents excite the system and the latter
can be estimated through the reverberation observed from the analysis of the
agents' opinions. The social network sensing problem can be interpreted as a
blind compressed sensing problem with a sparse measurement matrix. We prove
that the network structure will be revealed when a sufficient number of
stubborn agents independently influence a number of ordinary (non-stubborn)
agents. We investigate the scenario with a deterministic or randomized DeGroot
model and propose a consistent estimator of the steady states for the latter
scenario. Simulation results on synthetic and real world networks support our
findings.

Social and Information Networks;Machine Learning