Module stability 

FDboost-style stability selection over boosting base-learners (REG-06-05).

Wraps boost_fosr with a subsampling loop: B resamples of ⌊n/2⌋ rows (without replacement), aggregating per-base-learner selection frequencies. Base-learners with frequency ≥ π_thr are declared “stable”. The PFER bound is reported as an informational diagnostic.

Algorithm

For each resample b = 0..B:

1. Draw ⌊n/2⌋ distinct row indices without replacement, seeded by seed.wrapping_add(b) (per-replicate isolation → deterministic + parallel-safe).
2. Fit boost_fosr on the subsample.
3. Mark every base-learner that appears in the boosting path (selected_learners).

Selection frequency π̂[j] = (# resamples selecting j) / B. The stable set is { j : π̂[j] ≥ π_thr }. The Meinshausen–Bühlmann per-family-error-rate bound is E[V] ≤ q² / ((2·π_thr − 1)·p) where q is the mean per-subsample selection count.

References

Meinshausen & Bühlmann (2010). Stability Selection. JRSS-B, 72(4). Hofner et al. (2015). Controlling false discoveries in high-dimensional situations: Boosting with stability selection. The R Journal, 7(1).

Divergences from stabs (R package)

Uses subsampling ⌊n/2⌋ without replacement (Meinshausen-Bühlmann default). Selection criterion: base-learner appears in selected_learners at any iteration. Seeded per replicate for full reproducibility.

Functions

stability_selection

FDboost-style stability selection.