  We consider the problem of estimating causal DAG models from a mix of
observational and interventional data, when the intervention targets are
partially or completely unknown. This problem is highly relevant for example in
genomics, since gene knockout technologies are known to have off-target
effects. We characterize the interventional Markov equivalence class of DAGs
that can be identified from interventional data with unknown intervention
targets. In addition, we propose a provably consistent algorithm for learning
the interventional Markov equivalence class from such data. The proposed
algorithm greedily searches over the space of permutations to minimize a novel
score function. The algorithm is nonparametric, which is particularly important
for applications to genomics, where the relationships between variables are
often non-linear and the distribution non-Gaussian. We demonstrate the
performance of our algorithm on synthetic and biological datasets. Links to an
implementation of our algorithm and to a reproducible code base for our
experiments can be found at https://uhlerlab.github.io/causaldag/utigsp.
