essentialGraph function

Construct the essential graph

Constructs different versions of the essential graph from a given DAG. External function that computes essential graph of a dag Minimal PDAG: The only directed edges are those who participate in v-structure Completed PDAG: very directed edge corresponds to a compelled edge, and every undirected edge corresponds to a reversible edge

essentialGraph(dag, node.names = NULL, PDAG = "minimal")

Arguments

• dag: a matrix or a formula statement (see Details for format) defining the network structure, a directed acyclic graph (DAG).
• node.names: a vector of names if the DAG is given via formula, see Details .
• PDAG: a character value that can be: minimal or complete, see Details .

Returns

A matrix giving the PDAG.

Details

This function returns an essential graph from a DAG, aka acyclic partially directed graph (PDAG). This can be useful if the learning procedure is defined up to a Markov class of equivalence. A minimal PDAG is defined as only directed edges are those who participate in v-structure. Whereas the completed PDAG: every directed edge corresponds to a compelled edge, and every undirected edge corresponds to a reversible edge.

The dag can be provided using a formula statement (similar to glm). A typical formula is ~ node1|parent1:parent2 + node2:node3|parent3. The formula statement have to start with ~. In this example, node1 has two parents (parent1 and parent2). node2 and node3 have the same parent3. The parents names have to exactly match those given in node.names. : is the separator between either children or parents, | separates children (left side) and parents (right side), + separates terms, . replaces all the variables in node.names.

Examples

dag <- matrix(c(0,0,0, 1,0,0, 1,1,0), nrow = 3, ncol = 3)
dist <- list(a="gaussian", b="gaussian", c="gaussian")
colnames(dag) <- rownames(dag) <- names(dist)

essentialGraph(dag)

References

West, D. B. (2001). Introduction to Graph Theory. Vol. 2. Upper Saddle River: Prentice Hall. Chickering, D. M. (2013) A Transformational Characterization of Equivalent Bayesian Network Structures, arXiv:1302.4938.