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Causal relationships among a set of variables are commonly represented by adirected acyclic graph. The orientations of some edges in the causal DAG can bediscovered from observational/interventional data. Further edges can beoriented by iteratively applying so-called Meek rules. Inferring edges'orientations from some previously oriented edges, which we call CausalOrientation Learning (COL), is a common problem in various causal discoverytasks. In these tasks, it is often required to solve multiple COL problems andtherefore applying Meek rules could be time-consuming. Motivated by Meek rules,we introduce Meek functions that can be utilized in solving COL problems. Inparticular, we show that these functions have some desirable properties,enabling us to speed up the process of applying Meek rules. In particular, wepropose a dynamic programming (DP) based method to apply Meek functions.Moreover, based on the proposed DP method, we present a lower bound on thenumber of edges that can be oriented as a result of intervention. We alsopropose a method to check whether some oriented edges belong to a causal DAG.Experimental results show that the proposed methods can outperform previouswork in several causal discovery tasks in terms of running-time.

Fast Causal Orientation Learning in Directed Acyclic Graphs