lfhtcIdentifyStep {SEMID}

Perform one iteration of latent-factor HTC identification.

Description

A function that does one step through all the nodes in a latent-factor graph and tries to identify new edge coefficients using the existence of latent-factor half-trek systems.

Usage

lfhtcIdentifyStep(
  graph,
  unsolvedParents,
  solvedParents,
  activeFroms,
  Zs,
  Ls,
  identifier,
  subsetSizeControl = Inf
)

Arguments

graph

a LatentDigraph object representing the latent-factor graph. All latent nodes in this graph should be source nodes (i.e. have no parents).

unsolvedParents

a list whose ith index is a vector of all the parents j of i in the graph 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).

activeFroms

list. If node i is solved then the ith index is a vector containing the nodes Y otherwise it is empty.

Zs

list. If node i is solved then the ith index is a vector containing the nodes Z otherwise it is empty.

Ls

list. If node i is solved then the ith index is a vector containing the nodes Z otherwise it is empty.

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 latent-factor graph) and returns a list with two named arguments

subsetSizeControl

the largest subset of latent nodes to consider.

Value

a list with four components:

identifiedEdges

a matrix rx2 matrix where r is the number of edges that where identified by this function call and identifiedEdges[i,1] -> identifiedEdges[i,2] was the ith edge identified

unsolvedParents

as the input argument but updated with any newly identified edges

solvedParents

as the input argument but updated with any newly identified edges

identifier

as the input argument but updated with any newly identified edges

activeFroms

as the input argument but updated with any newly solved node

Zs

as the input argument but updated with any newly solved node

Ls

as the input argument but updated with any newly solved node

References

Barber, R. F., Drton, M., Sturma, N., and Weihs L. (2022). Half-Trek Criterion for Identifiability of Latent Variable Models. arXiv preprint arXiv:2201.04457