{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "The Scientific and Technological Research Council of Türkiye (TÜBİTAK), Informatics and Information Security Research Center (BİLGEM), 41470 Gebze, Kocaeli, Türkiye",
    "Software Engineering Department, Kocaeli University, Umuttepe, 41001 Izmit, Kocaeli, Türkiye"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Seda Kul",
      "orcid": "0000-0002-7481-3560"
    },
    {
      "affs": [
        1
      ],
      "name": "Mehmet Zeki Konyar",
      "orcid": "0000-0001-8914-5553"
    },
    {
      "affs": [
        1
      ],
      "name": "Kaplan Kaplan",
      "orcid": "0000-0001-8036-1145"
    },
    {
      "affs": [
        1
      ],
      "name": "Kerem Küçük",
      "orcid": "0000-0002-2621-634X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4d02hxek3wkn.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213988",
  "fulltext_url": null,
  "id": "a4d02hxek3wkn",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3988",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/a4d02hxek3wkn.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T00:23:28Z",
      "native_id": "10.3390/math14213988",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3988"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets",
  "title_text": "PAIR: Conditional Support Repair of Square-Root Allocations Under Fixed Data Budgets",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T00:20:49Z",
  "url": "https://research.draconitic.com/paper/a4d02hxek3wkn",
  "venue": "Mathematics",
  "versions": []
}