bnlearn (version 3.1)

cpdag: Equivalence classes, moral graphs and consistent extenions

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 = FALSE, debug = FALSE)
cextend(x, debug = FALSE)
vstructs(x, arcs = FALSE, moral = FALSE, 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.

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 parameter.

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 is confusing.

Setting moral to TRUE in cpdag and vstructs makes those functions follow the definition from Koller and Friedman (2009); the default value of FALSE, on the other hand, makes those functions follow the definition from Pearl (2000).

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 (2000). Causality: Models, Reasoning and Inference. Cambridge University Press.

Examples

data(learning.test)
res = gs(learning.test)
cpdag(res)
#
#   Bayesian network learned via Constraint-based methods
#
#   model:
#     [partially directed graph]
#   nodes:                                 6
#   arcs:                                  5
#     undirected arcs:                     1
#     directed arcs:                       4
#   average markov blanket size:           2.33
#   average neighbourhood size:            1.67
#   average branching factor:              0.67
#
#   learning algorithm:                    Grow-Shrink
#   conditional independence test:         Mutual Information (discrete)
#   alpha threshold:                       0.05
#   tests used in the learning procedure:  43
#   optimized:                             TRUE
#
vstructs(res)
#      X   Z   Y
# [1,] "A" "D" "C"
# [2,] "B" "E" "F"