Construct the essential graph
Constructs different versions of the essential graph from a given DAG
essentialGraph(dag, node.names = NULL, PDAG = "minimal")
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’. |
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.
A matrix giving the PDAG.
Gilles Kratzer
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.
Further information about abn can be found at:
http://r-bayesian-networks.org
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)
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