{
  "abstract": "In the era of big data, large-scale, multi-source, multi-modality datasets are increasingly ubiquitous, offering unprecedented opportunities for predictive modeling and scientific discovery. However, these datasets often exhibit complex heterogeneity, such as covariates shift, posterior drift, and blockwise missingness, which worsen predictive performance of existing supervised learning algorithms. To address these challenges simultaneously, we propose a novel Representation Retrieval ( R2 ) framework, which integrates a dictionary of representation learning modules (representer dictionary) with data source-specific sparsityinduced machine learning model (learners). Under the R2 framework, we introduce the notion of integrativeness for each representer, and propose a novel Selective Integration Penalty (SIP) to explicitly encourage more integrative representers to improve predictive performance. Theoretically, we show that the excess risk bound of the R2 framework is characterized by the integrativeness of representers, and SIP effectively improves the excess risk. Extensive simulation studies validate the superior performance of R2 framework and the effect of SIP. We further apply our method to two real-world datasets to confirm its empirical success. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Statistics & Data Science, Carnegie Mellon University, Pittsburgh, PA.",
    "Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qi Xu",
      "orcid": "0000-0003-1127-6523"
    },
    {
      "affs": [
        1
      ],
      "name": "Annie Qu",
      "orcid": "0000-0002-8396-7828"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7h7tyzys8pmy.bib",
  "cited_by": 17,
  "doi": "10.1080/01621459.2026.2696485",
  "fulltext_url": "https://europepmc.org/articles/PMC13645369",
  "id": "f7h7tyzys8pmy",
  "issns": [
    "0162-1459",
    "1537-274X"
  ],
  "landing_url": "https://europepmc.org/article/MED/42846695",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W4416031432",
  "pdf_url": "https://europepmc.org/articles/PMC13645369?pdf=render",
  "pmcid": "PMC13645369",
  "pmid": "42846695",
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7h7tyzys8pmy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:10Z",
      "native_id": "MED:42846695",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42846695"
    },
    {
      "first_seen": "2026-11-07T13:20:41Z",
      "native_id": "W4416031432",
      "source": "openalex",
      "url": "https://doi.org/10.1080/01621459.2026.2696485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Methods and Inference",
      "subfield": "statistics"
    }
  ],
  "title": "Representation Retrieval Learning for Heterogeneous Data Integration.",
  "title_text": "Representation Retrieval Learning for Heterogeneous Data Integration.",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/f7h7tyzys8pmy",
  "venue": "Journal of the American Statistical Association",
  "versions": []
}