lfhtcIdentifyStep: 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
)

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

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.

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