  One of the common obstacles for learning causal models from data is that
high-order conditional independence (CI) relationships between random variables
are difficult to estimate. Since CI tests with conditioning sets of low order
can be performed accurately even for a small number of observations, a
reasonable approach to determine casual structures is to base merely on the
low-order CIs. Recent research has confirmed that, e.g. in the case of sparse
true causal models, structures learned even from zero- and first-order
conditional independencies yield good approximations of the models. However, a
challenging task here is to provide methods that faithfully explain a given set
of low-order CIs. In this paper, we propose an algorithm which, for a given set
of conditional independencies of order less or equal to $k$, where $k$ is a
small fixed number, computes a faithful graphical representation of the given
set. Our results complete and generalize the previous work on learning from
pairwise marginal independencies. Moreover, they enable to improve upon the 0-1
graph model which, e.g. is heavily used in the estimation of genome networks.
