getMaxFlow {SEMID}

Size of largest HT system Y satisfying the HTC for a node v except perhaps having |getParents(v)| < |Y|.

Description

For an input mixed graph H, constructs the Gflow graph as described in Foygel et al. (2012) for a subgraph G of H. A max flow algorithm is then run on Gflow to determine the largest half-trek system in G to a particular node's getParents given a set of allowed nodes. Here G should consist of a bidirected part and nodes which are not in the bidirected part but are a parent of some node in the bidirected part. G should contain the node for which to compute the max flow.

Usage

getMaxFlow(L, O, allowedNodes, biNodes, inNodes, node)

Arguments

L

Adjacency matrix for the directed part of the path diagram/mixed graph; an edge pointing from i to j is encoded as L[i,j]=1 and the lack of an edge between i and j is encoded as L[i,j]=0. There should be no directed self loops, i.e. no i such that L[i,i]=1.

O

Adjacency matrix for the bidirected part of the path diagram/mixed graph. Edges are encoded as for the L parameter. Again there should be no self loops. Also this matrix will be coerced to be symmetric so it is only necessary to specify an edge once, i.e. if O[i,j]=1 you may, but are not required to, also have O[j,i]=1.

allowedNodes

the set of allowed nodes.

biNodes

the set of nodes in the subgraph G which are part of the bidirected part.

inNodes

the nodes of the subgraph G which are not in the bidirected part but are a parent of some node in the bidirected component.

node

the node (as an integer) for which the maxflow the largest half trek system

Value

See title.

References

Foygel, R., Draisma, J., and Drton, M. (2012) Half-trek criterion for generic identifiability of linear structural equation models. Ann. Statist. 40(3): 1682-1713.