{
  "abstract": "Estimating causal effects with continuous treatments in observational studies is challenging due to confounding, model misspecification, and high-dimensional covariates. We propose the Weighted Spline-Expanded Network (WSENet), an end-to-end neural framework that addresses these challenges by combining covariate balancing, structured treatment embedding, and bias-corrected outcome estimation. WSENet first applies Distance Covariate Optimal Weights to induce distributional independence between covariates and treatment without relying on parametric models. It then learns the conditional outcome via a structured network that fuses outcome-relevant representations of covariates with a spline-expanded treatment input, enabling smooth and flexible modeling of the dose-response relationship. To mitigate residual bias, we introduce Weighted Targeted Regularization, a correction technique based on efficient influence functions that yields a doubly robust estimator. Extensive evaluations on semi-synthetic and real-world datasets, including high-dimensional genomic and environmental health data, demonstrate that WSENet consistently outperforms existing baselines in both accuracy and stability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33740",
  "author_total": 3,
  "authors": [
    {
      "name": "Shucheng Liu"
    },
    {
      "name": "Chan Park"
    },
    {
      "name": "Guanhua Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3stpcjqshescv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33740",
  "fulltext_url": null,
  "id": "3stpcjqshescv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33740",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7214722914",
  "pdf_url": "https://arxiv.org/pdf/2609.33740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3stpcjqshescv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.33740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33740"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects",
  "title_text": "Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/3stpcjqshescv",
  "venue": "arXiv",
  "versions": []
}