bnlearn (version 4.1)

cpdag: Equivalence classes, moral graphs and consistent extensions

Description

Find the equivalence class and the v-structures of a Bayesian network, construct its moral graph, or create a consistent extension of an equivalent class.

Usage

cpdag(x, moral = TRUE, wlbl = FALSE, debug = FALSE)
cextend(x, strict = TRUE, debug = FALSE)
vstructs(x, arcs = FALSE, moral = TRUE, debug = FALSE)
moral(x, debug = FALSE)

Arguments

x

an object of class bn.

arcs

a boolean value. If TRUE the arcs that are part of at least one v-structure are returned instead of the v-structures themselves.

moral

a boolean value. If TRUE we define a v-structure as in Pearl (2000); if FALSE, as in Koller and Friedman (2009). See below.

wlbl

a boolean value. If TRUE arcs whose directions have been fixed by a whitelist or a by blacklist are preserved when constructing the CPDAG.

strict

a boolean value. If no consistent extension is possible and strict is TRUE, an error is generated; otherwise a partially extended graph is returned with a warning.

debug

a boolean value. If TRUE a lot of debugging output is printed; otherwise the function is completely silent.

Value

cpdag returns an object of class bn, representing the equivalence class. moral on the other hand returns the moral graph. See bn-class for details. cextend returns an object of class bn, representing a DAG that is the consistent extension of x. vstructs returns a matrix with either 2 or 3 columns, according to the value of the arcs argument.

Details

What kind of arc configuration is called a v-structure is not uniquely defined in literature. The original definition from Pearl (2000), which is still followed by most texts and papers, states that the two parents in the v-structure must not be connected by an arc. However, Koller and Friedman (2009) call that a immoral v-structure and call a moral v-structure a v-structure in which the parents are linked by an arc. This mirrors the unshielded versus shielded collider naming convention, but it is confusing. Setting moral to FALSE in cpdag and vstructs makes those functions follow the definition from Koller and Friedman (2009); the default value of TRUE, on the other hand, makes those functions follow the definition from Pearl (2000). The former call v-structures both shielded and unshielded colliders (respectively moral v-structures and immoral v-structures); the latter requires v-structures to be unshielded colliders. Note that arcs whose directions are dictated by the parametric assumptions of conditional linear Gaussian networks are preserved as directed arcs in cpdag.

References

Dor D (1992). A Simple Algorithm to Construct a Consistent Extension of a Partially Oriented Graph. UCLA, Cognitive Systems Laboratory. Available as Technical Report R-185. Koller D, Friedman N (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press. Pearl J (2009). Causality: Models, Reasoning and Inference. Cambridge University Press, 2nd edition.

Examples

data(learning.test)
res = gs(learning.test)
cpdag(res)
vstructs(res)