tpc (version 1.0)

MeekRules: Last Step of tPC Algorithm: Apply Meek's rules

Description

This is a modified version of pcalg::udag2pdagRelaxed. It applies Meek's rules to the partially oriented graph obtained after orienting edges between time points / tiers.

Usage

MeekRules(
  gInput,
  verbose = FALSE,
  unfVect = NULL,
  solve.confl = FALSE,
  rules = rep(TRUE, 4)
)

Value

An object of class pcAlgo-class.

Arguments

gInput

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

verbose

FALSE: No output; TRUE: Details

unfVect

Vector containing numbers that encode ambiguous triples (as returned by [tpc_cons_intern()]. This is needed in the conservative and majority rule PC algorithms.

solve.confl

If TRUE, 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.

rules

A vector of length 4 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.

Author

Original code by Markus Kalisch, modifications by Janine Witte.

Details

If unfVect = NULL (no ambiguous triples), the four orientation rules are applied to each eligible structure until no more edges can be oriented. Otherwise, unfVect contains the numbers of all ambiguous triples in the graph as determined by [tpc_cons_intern()]. Then the orientation rules take this information into account. For example, if a -> b - c and <a,b,c> is an unambigous triple and a non-v-structure, then rule 1 implies b -> c. On the other hand, if a -> b - c but <a,b,c> is an ambiguous triple, then the edge b - c is not oriented.

If solve.confl = FALSE, earlier edge orientations are overwritten by later ones.

If solv.confl = TRUE, both the v-structures and the orientation rules work with lists for the candidate edges and allow bi-directed edges if there are conflicting orientations. For example, two v-structures a -> b <- c and b -> c <- d then yield a -> b <-> c <- d. This option can be used to get an order-independent version of the PC algorithm (see Colombo and Maathuis (2014)).

We denote bi-directed edges, for example between two variables i and j, in the adjacency matrix M of the graph as M[i,j]=2 and M[j,i]=2. Such edges should be interpreted as indications of conflicts in the algorithm, for example due to errors in the conditional independence tests or violations of the faithfulness assumption.

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.

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

Examples

data(dat_sim)
sk.fit <- skeleton(suffStat = list(C = cor(dat_sim), n = nrow(dat_sim)),
             indepTest = gaussCItest, labels = names(dat_sim), alpha = 0.05)
MeekRules(sk.fit)