  This paper addresses the problem of inferring sparse causal networks modeled
by multivariate auto-regressive (MAR) processes. Conditions are derived under
which the Group Lasso (gLasso) procedure consistently estimates sparse network
structure. The key condition involves a "false connection score." In
particular, we show that consistent recovery is possible even when the number
of observations of the network is far less than the number of parameters
describing the network, provided that the false connection score is less than
one. The false connection score is also demonstrated to be a useful metric of
recovery in non-asymptotic regimes. The conditions suggest a modified gLasso
procedure which tends to improve the false connection score and reduce the
chances of reversing the direction of causal influence. Computational
experiments and a real network based electrocorticogram (ECoG) simulation study
demonstrate the effectiveness of the approach.
