  A method of `network filtering' has been proposed recently to detect the
effects of certain external perturbations on the interacting members in a
network. However, with large networks, the goal of detection seems a priori
difficult to achieve, especially since the number of observations available
often is much smaller than the number of variables describing the effects of
the underlying network. Under the assumption that the network possesses a
certain sparsity property, we provide a formal characterization of the accuracy
with which the external effects can be detected, using a network filtering
system that combines Lasso regression in a sparse simultaneous equation model
with simple residual analysis. We explore the implications of the technical
conditions underlying our characterization, in the context of various network
topologies, and we illustrate our method using simulated data.
