Extract the ancestor sets M(x_i) for every variable

Faithful port of rcd.py's extract_ancestors() (original 254-316 lines). Repeatedly scans variable subsets of increasing size, growing each variable's ancestor set whenever a unique "sink" is found within a subset. See dev/rcd-implementation.md section 3.2 for the full algorithm description and the reasoning behind the cache-update position.

Usage

extract_ancestors(
  X,
  max_explanatory_num,
  cor_alpha,
  ind_alpha,
  shapiro_alpha,
  MLHSICR,
  independence,
  ind_corr
)

Arguments

X

(uncentered) data matrix

max_explanatory_num

maximum subset size minus 1

cor_alpha

correlation-test significance level

ind_alpha

independence-test significance level (hsic)

shapiro_alpha

non-Gaussianity significance level

MLHSICR

whether to use MLHSICR regression as a fallback

independence

"hsic" or "fcorr"

ind_corr

F-correlation rejection threshold (fcorr)

Value

list of length ncol(X); each element is a sorted integer vector of ancestor indices (possibly empty)