cpdag: Equivalence classes, moral graphs and consistent extensions

In bnlearn: Bayesian Network Structure Learning, Parameter Learning and Inference

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

cextend.all(x, debug = FALSE)

colliders(x, arcs = FALSE, debug = FALSE)
shielded.colliders(x, arcs = FALSE, debug = FALSE)
unshielded.colliders(x, arcs = FALSE, debug = FALSE)
vstructs(x, arcs = FALSE, debug = FALSE)

Arguments

x	an object of class bn or bn.fit (with the exception of cextend(), which only accepts objects 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.
wlbl	a boolean value. If TRUE, arcs whose directions have been fixed by a whitelist or a 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.

Details

Note that arcs whose directions are dictated by the parametric assumptions of the network are preserved as directed arcs in cpdag(). This means that, in a conditional Gaussian network, arcs from discrete nodes to continuous nodes will be treated as whitelisted in their only valid direction.

cextend.all() returns all possible consistent extensions of a CPDAG, whereas cextend() returns only one. cextend.all() also accepts a PDAG or an MPDAG (a partially directed graph carrying background knowledge, in which some directed arcs are not compelled), in which case it enumerates the consistent extensions that agree with the given arc directions; it stops with an error if no such extension exists.

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.

cextend.all() returns an object of class bn or a list of objects of class bn.

vstructs(), colliders(), shielded.colliders() and unshielded.colliders() return a matrix with either 2 or 3 columns, according to the value of the arcs argument.

Author(s)

Marco Scutari

References

Dor D (1992). A Simple Algorithm to Construct a Consistent Extension of a Partially Oriented Graph. UCLA, Cognitive Systems Laboratory.

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.

Andersson SA, Madigan D, Perlman MD (1997). "A Characterization of Markov Equivalence Classes for Acyclic Digraphs." The Annals of Statistics, 25(2):505–541.

Wienobst M, Luttermann M, Bannach M, Liskiewicz M (2023). "Efficient Enumeration of Markov Equivalent DAGs." Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence, 12313–12320.

Examples

data(learning.test)
dag = hc(learning.test)
cpdag(dag)
vstructs(dag)

bnlearn documentation built on July 17, 2026, 5:08 p.m.