{
  "abstract": "Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computational constraints demand compact yet faithful summaries. A standard approach is to construct an \\textit{$ε$-coreset}: a small weighted subset that approximately preserves the clustering cost for every plausible choice of centers. For the \\textit{$(k,z)$-clustering problem}, existing worst-case bounds on coreset size are essentially tight, ruling out substantially smaller coresets in general. However, such worst-case instances are often unrepresentative of real-world data. In this work, we show that significantly smaller coresets are possible under mild and natural assumptions on the underlying data distribution. We introduce a new correlated sampling framework, called \\textit{determinantal sampling}, based on a novel application of determinantal point processes. Using this framework, we obtain an efficiently constructible $\\varepsilon$-coreset for $(k,z)$-clustering in $\\mathbb R^d$ whose dependence on $1/\\varepsilon$ has exponent strictly smaller than $2$ when $d$ is fixed. This improves over the worst-case $\\varepsilon^{-2}$ barrier under our beyond-worst-case assumptions. To the best of our knowledge, this is the first result that provably surpasses these lower bounds through beyond-worst-case assumptions. Finally, we validate our approach on synthetic and real-world benchmark datasets, where it consistently achieves smaller coresets than existing state-of-the-art methods, even without explicitly enforcing the assumptions used in the analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06394",
  "author_total": 4,
  "authors": [
    {
      "name": "Diptarka Chakraborty"
    },
    {
      "name": "Satyaki Mukherjee"
    },
    {
      "name": "Gaurav Vallabhdas Revankar"
    },
    {
      "name": "Hoang-Son Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at6hxqq10mwq2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06394",
  "fulltext_url": null,
  "id": "at6hxqq10mwq2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06394",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Clustering Algorithms Research"
    ]
  ],
  "openalex": "W7212023603",
  "pdf_url": "https://arxiv.org/pdf/2609.06394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at6hxqq10mwq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06394"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond Worst-Case Coreset Bounds for $k$-Clustering via Determinantal Sampling",
  "title_text": "Beyond Worst-Case Coreset Bounds for k-Clustering via Determinantal Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/at6hxqq10mwq2",
  "venue": "arXiv",
  "versions": []
}