PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets
- 1The Scientific and Technological Research Council of Türkiye (TÜBİTAK), Informatics and Information Security Research Center (BİLGEM), 41470 Gebze, Kocaeli, Türkiye
- 2Software Engineering Department, Kocaeli University, Umuttepe, 41001 Izmit, Kocaeli, Türkiye
Abstract
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.
Related
- Optimal support and condensation in random allocations
- A prime plus a square: A conditional 11/20 upper bound
- Envy-Free Allocations for Random Non-Additive Valuations
- Monotone Allocations without Single-Crossing: When to Bunch and When to Jump
- Probability of Quota Violations in Divisor Apportionment Methods with Nonzero Allocations
BibTeX
@article{kul2026pair,
title = {{PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets}},
author = {Seda Kul and Mehmet Zeki Konyar and Kaplan Kaplan and Kerem Küçük},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14213988},
url = {https://www.mdpi.com/2227-7390/14/21/3988},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets
AU - Seda Kul
AU - Mehmet Zeki Konyar
AU - Kaplan Kaplan
AU - Kerem Küçük
PY - 2026
DA - 2026/11/02
JO - Mathematics
DO - 10.3390/math14213988
UR - https://www.mdpi.com/2227-7390/14/21/3988
AB - 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.
SN - 2227-7390
ER -