Group-Local Anchoring for Subgroup Intervals in Programmatic Weak Supervision

Programmatic weak supervision uses approximate labeling functions to construct training labels. Evaluating these labels requires intervals for class proportions within subgroups of an unlabeled pool. An existing approach derives such intervals from pool-wide statistics estimated using a small labeled sample. These global constraints can provide simultaneous coverage while leaving small-group intervals equal to the full probability range, because changes within a small group have little effect on pool-wide statistics. We study how labels reaching a subgroup determine interval precision. For binary labels, we derive a width lower bound from the pool-to-group size ratio and the room for variation allowed by the global constraints. This identifies a computable group-size threshold below which intervals must span the full probability range. Motivated by this bound, group-local anchoring adds constraints estimated from labeled observations within each group. Joint calibration preserves simultaneous coverage when group selection is independent of the estimation labels. For groups learned from labels, we use disjoint samples for selection and estimation. With 400 labeled draws from the pool, median global-to-anchored width ratios range from 1.21 to 1.69 across five text corpora, with gains concentrated in groups containing at least 32 pool instances. Experiments on text and image corpora further show that reusing selection labels for estimation produces coverage failures concentrated in selectors that memorize labels for individual labeling-function patterns. In the image experiments, independent estimation reduces this undercoverage. Median split-to-reference width ratios are 1.42–1.98, where the reference uses all acquired labels on the same groups. These results link subgroup precision to local labeling information and support independent estimation for learned groups.