  The PC algorithm is a popular method for learning the structure of Gaussian
Bayesian networks. It carries out statistical tests to determine absent edges
in the network. It is hence governed by two parameters: (i) The type of test,
and (ii) its significance level. These parameters are usually set to values
recommended by an expert. Nevertheless, such an approach can suffer from human
bias, leading to suboptimal reconstruction results. In this paper we consider a
more principled approach for choosing these parameters in an automatic way. For
this we optimize a reconstruction score evaluated on a set of different
Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a
closed-form expression, which means that Bayesian optimization (BO) is a
natural choice. BO methods use a model to guide the search and are hence able
to exploit smoothness properties of the objective surface. We show that the
parameters found by a BO method outperform those found by a random search
strategy and the expert recommendation. Importantly, we have found that an
often overlooked statistical test provides the best over-all reconstruction
results.
