Greedy relaxations of the sparsest permutation algorithm

There has been an increasing interest in methods that exploit permutation reasoning to search for directed acyclic causal models, including the “Ordering Search’’ of Teyssier and Kohler and GSP of Solus, Wang and Uhler. We extend the methods of the latter by a permutation-based operation tuck, and develop a class of algorithms, namely GRaSP, that are computationally efficient and pointwise consistent under increasingly weaker assumptions than faithfulness. The most relaxed form of GRaSP outperforms many state-of-the-art causal search algorithms in simulation, allowing efficient and accurate search even for dense graphs and graphs with more than 100 variables.