PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets

Downsampling an imbalanced training set to a fixed data budget requires deciding how many observations each class retains. Under aggressive compression, even Square-Root allocation can leave rare classes with only a few training observations. We introduce PAIR (Pair-Capacity Adaptive Intervention and Repair), a conditional support-repair operator that keeps capacity-aware Square-Root allocation as the parent solution. PAIR raises a structural-tail quota only when it falls below a K-dependent floor, optionally strengthened by a training-only representation criterion, and then restores the exact budget by minimum-divergence repair; otherwise, it returns the Square-Root quotas and sampled rows exactly. On NF-ToN-IoT, UNSW-NB15, and CICIDS2017 with budgets of 1000–5000, PAIR is active in four of nine settings and identical to Square-Root in the other five. Held-out Macro-F1 rises from 0.5227 to 0.5466 on NF-ToN-IoT at B=1000, where fixed Power is higher (0.5519), and from 0.6363, 0.6788, and 0.7626 to 0.6714, 0.7726, and 0.7945 on CICIDS2017, the highest of seven compared methods. PAIR exceeds Square-Root in 39 of 40 active repeated development-split comparisons, and a synthetic study confirms the closed-form activation condition. The CICIDS2017 gains concentrate in classes with two to seven held-out observations, while Accuracy and Weighted-F1 change by less than 0.002, indicating rare-event recovery.