Figure 1.

Structure learning: constraint-based algorithms search for trios of variables and test their relations with marginal and conditional independence tests. Thereby, they distinguish between the stochastic decomposition of the joint distribution of all variables as in (A) and the decomposition as in (B). These two decompositions can be represented in a DAG as shown. Whereas the directions are clear and unique in (B), the influences’ directions in (A) can form three different graphs. Which of these equivalent structures is most likely, one can only deduce from the context of other already tested decompositions in their neighborhood and from the rule that no cycles must be formed in the graph.