Almost Optimal Intervention Sets for Causal Discovery

We conjecture that the worst case number of experiments necessary and sufficient to discover a causal graph uniquely given its observational Markov equivalence class can be specified as a function of the largest clique in the Markov equivalence class. We provide an algorithm that computes intervention sets that we believe are optimal for the above task. The algorithm builds on insights gained from the worst case analysis in Eberhardt et al. (2005) for sequences of experiments when all possible directed acyclic graphs over N variables are considered. A simulation suggests that our conjecture is correct. We also show that a generalization of our conjecture to other classes of possible graph hypotheses cannot be given easily, and in what sense the algorithm is then no longer optimal.