  Learning directed acyclic graphs using both observational and interventional
data is now a fundamentally important problem due to recent technological
developments in genomics that generate such single-cell gene expression data at
a very large scale. In order to utilize this data for learning gene regulatory
networks, efficient and reliable causal inference algorithms are needed that
can make use of both observational and interventional data. In this paper, we
present two algorithms of this type and prove that both are consistent under
the faithfulness assumption. These algorithms are interventional adaptations of
the Greedy SP algorithm and are the first algorithms using both observational
and interventional data with consistency guarantees. Moreover, these algorithms
have the advantage that they are nonparametric, which makes them useful also
for analyzing non-Gaussian data. In this paper, we present these two algorithms
and their consistency guarantees, and we analyze their performance on simulated
data, protein signaling data, and single-cell gene expression data.
