Causal Graph Identification Under Soft Intervention

In this paper, causal graph identification with natural observations as well as observations due to soft interventions is investigated. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. The proposed causal graph learning approach is informed by prior work which proposed the decomposition of the problem into learning sub-graphs (all of the parents of a node) to learn the whole graph. A greedy algorithm that focuses on the reduction of the false negative rate (erroneously missing the presence of a causal relationship) is proposed. A sufficient condition is derived, under which the estimated graph is guaranteed to be free of false negatives, almost surely as the number of observations grows large. Numerical results indicate that the proposed scheme outperforms standard graph identification schemes by exploiting the sub-graph structure and by exploring a broader set of soft interventions. Compared to existing approaches, the proposed scheme achieves a 32% gain in false negative rate and a 62% gain in normalized Hamming distance.