Efficient Causal Structure Learning from Multiple Interventional Datasets with Unknown Targets

We consider the problem of reducing the false discovery rate in multiple high-dimensional interventional datasets under unknown targets. Traditional algorithms merged directly multiple causal graphs learned, which ignores the contradictions of different datasets, leading to lots of inconsistent directions of edges. For reducing the contradictory information, we propose a new algorithm, which first learns an interventional Markov equivalence class (I-MEC) before merging multiple graphs. It utilizes the full power of the constraints available in interventional data and combines ideas from local learning, intervention, and search-and-score techniques in a principled and effective way in different intervention experiments. Specifically, local learning on multiple datasets is used to build a causal skeleton. Perfect intervention destroys some possible triangles, leading to the identification of more possible V-structures. And then a theoretically correct I-MEC is learned. Search and scoring techniques based on the learned I-MEC further identify the remaining unoriented edges. Both theoretical analysis and experiments on benchmark Bayesian networks with the number of variables from 20 to 724 validate that the effectiveness of our algorithm in reducing the false discovery rate in high-dimensional interventional data.