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.
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)an object of class bn.
a boolean value. If TRUE the arcs that are part of at least
one v-structure are returned instead of the v-structures themselves.
a boolean value. If TRUE we define a v-structure as in
Pearl (2000); if FALSE, as in Koller and Friedman (2009). See below.
a boolean value. If TRUE arcs whose directions have been
fixed by a whitelist or a by blacklist are preserved when constructing
the CPDAG.
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.
a boolean value. If TRUE a lot of debugging output is
printed; otherwise the function is completely silent.
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.
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.
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.
data(learning.test)
res = gs(learning.test)
cpdag(res)
vstructs(res)
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