Recorded Sample Membership in Aggregate-Based Prediction Adjustment

Aggregate labels, the supervision used in learning from label proportions, can also correct a model's predictions after training. When a sample is altered by recorded replacements, knowing which instances were kept can rule out predictions that class counts alone allow. We study a setting in which a uniform sample from a group with known class totals is modified through recorded replacements. The central intervention acquires no new individual labels: it uses the retained collection record more fully. For one original subset, we derive an efficient compatibility test that determines whether the current prediction remains consistent with the full sampling record. When incompatibility is detected, the violated restrictions yield short corrections with computable lower bounds on average squared-loss improvement. We compare these corrections with full joint adjustment and with predictions already corrected using count-based aggregate bounds. A prespecified evaluation on 256 previously unused Covertype groups shows that membership-specific constraints can change predictions across several selection regimes. In the primary setting such corrections are rare, but they act on poorly predicted outputs, and short corrections recover most of the full adjustment's gain. A separate matched intervention shows that correcting an earlier prediction can discard improvement already present in the available incumbent. Together, the results give a cheap, certified way to tell when a sampling record justifies a further correction, with a guaranteed minimum improvement.