{
  "abstract": "We propose a Bayesian nonparametric factor model that infers the number of factors, induces row-wise sparsity, and merges redundant dictionary elements via exact clustering. A Dirichlet process prior is placed on the columns of an overcomplete loading matrix and fully marginalized to an exact Pólya urn, avoiding stick-breaking and auxiliary variables. A spike-and-slab base measure allows entire factors to be exactly zero. The model uniquely combines exact zeros, exchangeability over columns, and exact merging within a single marginalized Dirichlet process, unlike CUSP, MGP, or the beta process. An exact Gibbs sampler with canonical relabeling and parallel C/MPI implementation is developed. We prove posterior contraction at rate $\\sqrt{M s_0 \\log n / n}$ for the covariance matrix, and in the fixed-dictionary setting obtain the minimax optimal rate $\\sqrt{s_0 \\log n / n}$ plus underfitting consistency; the overfitting direction is an open conjecture. The spike-and-slab is essential: without it the effective dimension scales as $pM$, yielding a slower rate. Simulations show the method is the only fully adaptive approach to recover the true rank, achieving the smallest covariance, loading, and signal-reconstruction errors, beating an oracle baseline. On van 't Veer breast cancer data ($n=97$, $p=1213$), the posterior concentrates on eight interpretable programmes; seven pass coherence and two pass Bonferroni-corrected Hallmark enrichment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34546",
  "author_total": 2,
  "authors": [
    {
      "name": "Durba Bhattacharya"
    },
    {
      "name": "Sourabh Bhattacharya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1m5n65wgffywc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34546",
  "fulltext_url": null,
  "id": "1m5n65wgffywc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34546",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7214735718",
  "pdf_url": "https://arxiv.org/pdf/2609.34546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1m5n65wgffywc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Bayesian Nonparametric Factor Analysis via Marginalized Dirichlet Process Column Clustering with Spike-and-Slab Sparsity",
  "title_text": "Bayesian Nonparametric Factor Analysis via Marginalized Dirichlet Process Column Clustering with Spike-and-Slab Sparsity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/1m5n65wgffywc",
  "venue": "arXiv",
  "versions": []
}