  We consider structure learning of linear Gaussian structural equation models
with weak edges. Since the presence of weak edges can lead to a loss of edge
orientations in the true underlying CPDAG, we define a new graphical object
that can contain more edge orientations. We show that this object can be
recovered from observational data under a type of strong faithfulness
assumption. We present a new algorithm for this purpose, called aggregated
greedy equivalence search (AGES), that aggregates the solution path of the
greedy equivalence search (GES) algorithm for varying values of the penalty
parameter. We prove consistency of AGES and demonstrate its performance in a
simulation study and on single cell data from Sachs et al. (2005). The
algorithm will be made available in the R-package pcalg.
