  We consider the problem of learning causal DAGs in the setting where both
observational and interventional data is available. This setting is common in
biology, where gene regulatory networks can be intervened on using chemical
reagents or gene deletions. Hauser and B\"uhlmann (2012) previously
characterized the identifiability of causal DAGs under perfect interventions,
which eliminate dependencies between targeted variables and their direct
causes. In this paper, we extend these identifiability results to general
interventions, which may modify the dependencies between targeted variables and
their causes without eliminating them. We define and characterize the
interventional Markov equivalence class that can be identified from general
(not necessarily perfect) intervention experiments. We also propose the first
provably consistent algorithm for learning DAGs in this setting and evaluate
our algorithm on simulated and biological datasets.
