docs.javahelp.manual.boxes.search.pcd.html Maven / Gradle / Ivy
Search Algorithms: PC
Search Algorithms: PCD
PCD is a modification of the PC algorithm that allows it to search over datasets in which some of the
variables stand in deterministic relationships. A deterministic relationship between variables is one that is purely
functional, with no random variation involved. For instance, if X = 2Y, then X and Y in the graph X<--Y-->Z
stand in a deterministic relationships. The PC algorithm does not deal well with examples of this sort. For
instance, the PC algorithm might do a statistical test to determine whether X _||_ Z | Y, in order to see whehter
the edge X---Z should be removed during the adjacency phase. But since X and Y stand in a deterministic
relationship, it is always the case that X _||_ Z | Y, since this is informationally equivalent to asking whether X
_||_ Z | X, which is always true. But establishing that X _||_ Z | X is never a good reason for removing the edge
between X and Z; if such a reason were permitted, the adjacency phase of the PC search would always return an empty
graph! In the face of deterministic relationships, the PC algorithm needs to be made aware of when effective
conditioning on an endpoint of an edge happens and adjustements need to be made to prevent edges from being
eliminated for such reasons.
To correct the problem, PCD checks before performing an independence check of the form X _||_ Z | S, whether X
determines either X or Y, and if it does, refuses to do the independence check. This correct the problem for the
adjacency search. There is an additional problem in the step where colliderDiscovery are oriented. In this case,
PCD, when
considering whether to orient an unshielded triple <X, Y, Z> as a collider, based on a conderation of the set
Sxz that was used to remove the edge X---Z from the graph during the adjacency search, first asks whether Sxz
determines X or Y. If it does not, then <X, Y, Z> is oriented as a collider X-->Y<--Z if Y is not
contained in Sxz.
Otherwise, the assumptions and types of data permitted for PCD are identical to that of PC.
?