{
  "abstract": "Semiparametric Bayesian networks (SPBNs) are flexible probabilistic graphical models for representing joint distributions of continuous variables through lower-dimensional conditional probability distributions (CPDs). Existing SPBN models use kernel density estimators (KDEs) for non-parametric CPD modeling, but their one-component-per-observation mixture representation can lead to increased inference costs and density estimation errors, which can be limiting. In this work, we define a new CPD modeling approach for non-parametric components based on Bayesian non-parametric Dirichlet Process Mixtures (DPMs) within SPBNs. DPMs provide a data-adaptive clustering of observations, yielding a more compact representation while retaining the flexibility of non-parametric density estimation, unlike KDE. This results in lower inference costs while improving density estimation performance. We implement the proposed DPM-based SPBN (DPM-SPBN) by extending the open-source PyBNesian package and evaluate it on synthetic and real-world data. For a given network structure, DPM-based CPDs significantly outperform state-of-the-art Bayesian network models for continuous variables in density estimation, achieving lower absolute log-likelihood errors on synthetic data. We further investigate the impact of the proposed CPD modeling on structure learning methods relying on CPD-based scores. DPM-based SPBNs achieve lower structure learning and density estimation errors than KDE-based SPBNs. Experiments on real-world data corroborate these findings, identifying DPM-based CPD modeling as the most effective alternative among the evaluated non-parametric approaches for continuous variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36110",
  "author_total": 3,
  "authors": [
    {
      "name": "Victor Alejandre"
    },
    {
      "name": "Pedro Larrañaga"
    },
    {
      "name": "Concha Bielza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddj574ghkawds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36110",
  "fulltext_url": null,
  "id": "ddj574ghkawds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36110",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.36110",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddj574ghkawds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:59Z",
      "native_id": "2610.36110",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36110"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach",
  "title_text": "Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/ddj574ghkawds",
  "venue": "arXiv",
  "versions": []
}