  Graphical causal models are an important tool for knowledge discovery because
they can represent both the causal relations between variables and the
multivariate probability distributions over the data. Once learned, causal
graphs can be used for classification, feature selection and hypothesis
generation, while revealing the underlying causal network structure and thus
allowing for arbitrary likelihood queries over the data. However, current
algorithms for learning sparse directed graphs are generally designed to handle
only one type of data (continuous-only or discrete-only), which limits their
applicability to a large class of multi-modal biological datasets that include
mixed type variables. To address this issue, we developed new methods that
modify and combine existing methods for finding undirected graphs with methods
for finding directed graphs. These hybrid methods are not only faster, but also
perform better than the directed graph estimation methods alone for a variety
of parameter settings and data set sizes. Here, we describe a new conditional
independence test for learning directed graphs over mixed data types and we
compare performances of different graph learning strategies on synthetic data.
