  Structure learning methods for covariance and concentration graphs are often
validated on synthetic models, usually obtained by randomly generating: (i) an
undirected graph, and (ii) a compatible symmetric positive definite (SPD)
matrix. In order to ensure positive definiteness in (ii), a dominant diagonal
is usually imposed. However, the link strengths in the resulting graphical
model, determined by off-diagonal entries in the SPD matrix, are in many
scenarios extremely weak. Recovering the structure of the undirected graph thus
becomes a challenge, and algorithm validation is notably affected. In this
paper, we propose an alternative method which overcomes such problem yet
yielding a compatible SPD matrix. We generate a partially row-wise-orthogonal
matrix factor, where pairwise orthogonal rows correspond to missing edges in
the undirected graph. In numerical experiments ranging from moderately dense to
sparse scenarios, we obtain that, as the dimension increases, the link strength
we simulate is stable with respect to the structure sparsity. Importantly, we
show in a real validation setting how structure recovery is greatly improved
for all learning algorithms when using our proposed method, thereby producing a
more realistic comparison framework.
