edgewiseIdentifyStep {SEMID}

Perform one iteration of edgewise identification.

Description

A function that does one step through all the nodes in a mixed graph and tries to identify new edge coefficients using the existence of half-trek systems as described in Weihs, Robeva, Robinson, et al. (2017).

Usage

edgewiseIdentifyStep(
  mixedGraph,
  unsolvedParents,
  solvedParents,
  identifier,
  subsetSizeControl = Inf
)

Arguments

mixedGraph

a MixedGraph object representing the mixed graph.

unsolvedParents

a list whose ith index is a vector of all the parents j of i in G which for which the edge j->i is not yet known to be generically identifiable.

solvedParents

the complement of unsolvedParents, a list whose ith index is a vector of all parents j of i for which the edge i->j is known to be generically identifiable (perhaps by other algorithms).

identifier

an identification function that must produce the identifications corresponding to those in solved parents. That is identifier should be a function taking a single argument Sigma (any generically generated covariance matrix corresponding to the mixed graph) and returns a list with two named arguments

Lambda

denote the number of nodes in mixedGraph as n. Then Lambda is an nxn matrix whose i,jth entry

1. equals 0 if i is not a parent of j,

2. equals NA if i is a parent of j but identifier cannot identify it generically,

3. equals the (generically) unique value corresponding to the weight along the edge i->j that was used to produce Sigma.

Omega

just as Lambda but for the bidirected edges in the mixed graph

such that if j is in solvedParents[[i]] we must have that Lambda[j,i] is not NA.

subsetSizeControl

a positive integer (Inf allowed) which controls the size of edgesets searched in the edgewiseID algorithm. Suppose, for example, this has value 3. Then if a node i has n parents, this will restrict the algorithm to only look at subsets of the parents of size 1,2,3 and n-2, n-1, n. Making this parameter smaller means the algorithm will be faster but less exhaustive (and hence less powerful).

Value

see the return of htcIdentifyStep.