pcalg (version 2.4-3)

udag2pdag: Last PC Algorithm Step: Extend Object with Skeleton to Completed PDAG

Description

These functions perform the last step in the PC algorithm: Transform an object of the class "pcAlgo" containing a skeleton and corresponding conditional independence information into a completed partially directed acyclic graph (CPDAG). The functions first determine the v-structures, and then apply the three orientation rules as described in Sprirtes et al (2000) and Meek (1995) to orient as many of the remaining edges as possible.

In the oracle version and when all assumptions hold, all three functions yield the same CPDAG. In the sample version, however, the resulting CPDAG may be invalid in the sense that one cannot extend it a DAG without additional unshielded colliders by orienting the undirecting edges. This can for example happen due to errors in the conditional indepedence tests or violations of the faithfulness assumption. The three functions deal with such conflicts in different ways, as described in Details.

Usage

udag2pdag       (gInput, verbose)
udag2pdagRelaxed(gInput, verbose, unfVect=NULL, solve.confl=FALSE, orientCollider = TRUE, rules = rep(TRUE, 3))
udag2pdagSpecial(gInput, verbose, n.max=100)

Arguments

gInput

"pcAlgo"-object containing skeleton and conditional indepedence information.

verbose

0: No output; 1: Details

unfVect

vector containing numbers that encode ambiguous triples (as returned by pc.cons.intern). This is needed in the conservative and majority rule PC algorithms.

solve.confl

if TRUE, the orientation of the v-structures and the orientation rules work with lists for candidate sets and allow bi-directed edges to resolve conflicting edge orientations. Note that therefore the resulting object is order-independent but might not be a PDAG because bi-directed edges can be present.

n.max

maximum number of tries for re-orienting doubly visited edges in udag2pdagSpecial.

orientCollider

if TRUE, collider are oriented.

rules

Array of length 3 containing TRUE or FALSE for each rule. TRUE in position i means that rule i (Ri) will be applied. By default, all rules are used.

Value

Details

References

C. Meek (1995). Causal inference and causal explanation with background knowledge. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), pp. 403-411. Morgan Kaufmann Publishers, Inc.

P. Spirtes, C. Glymour and R. Scheines (2000) Causation, Prediction, and Search, 2nd edition, The MIT Press.

J. Pearl (2000), Causality, Cambridge University Press.

D. Colombo and M.H. Maathuis (2014).Order-independent constraint-based causal structure learning. Journal of Machine Learning Research 15 3741-3782.

See Also

pc, pdag2dag, dag2cpdag, udag2pag, udag2apag, dag2pag.

Examples

## simulate data
set.seed(123)
p <- 10
myDAG <- randomDAG(p, prob = 0.2)
trueCPDAG <- dag2cpdag(myDAG)
n <- 1000
d.mat <- rmvDAG(n, myDAG, errDist = "normal")

## estimate skeleton
resU <- skeleton(suffStat = list(C = cor(d.mat), n = n),
                 indepTest = gaussCItest, ## (partial correlations)
                 alpha = 0.05, p=p)

## orient edges using three different methods
resD1 <- udag2pdagRelaxed(resU, verbose=0)
resD2 <- udag2pdagSpecial(resU, verbose=0, n.max=100)
resD3 <- udag2pdag       (resU, verbose=0)