{
  "abstract": "Distribution regression seeks to learn mappings from probability distributions to response variables and has emerged as a unifying framework for kernel methods, multi-instance learning, and set-valued learning. Despite its success, kernel-based distribution regression remains computationally expensive and sensitive to kernel choice, motivating scalable and adaptive representations. Building on random feature approximations, we develop a finite-sample analysis of Random Feature Distribution Regression (RaDR) under two-stage sampling. Our perturbation analysis separates the effects of distribution-level sampling, finite within-bag sampling, and random feature approximation. We establish sufficient feature-budget conditions under which RaDR preserves the order of our excess-risk upper bound for exact two-stage kernel distribution regression while maintaining computational efficiency. We further propose Adaptive Random Feature Distribution Regression (A-RaDR), a unified score-guided framework that adaptively allocates random features according to downstream learning objectives. Experiments on synthetic benchmarks and 41 real-world datasets demonstrate that RaDR delivers substantial computational savings while maintaining competitive predictive performance, whereas A-RaDR further improves learning accuracy in distribution regression while retaining the computational speed up. Together, these results establish a practical and theoretically grounded framework for adaptive, scalable distribution learning",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24892",
  "author_total": 3,
  "authors": [
    {
      "name": "Yinsong Wang"
    },
    {
      "name": "Xiao Liu"
    },
    {
      "name": "Yu Ding"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fvkspkpzb4t0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24892",
  "fulltext_url": null,
  "id": "4fvkspkpzb4t0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24892",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7223071055",
  "pdf_url": "https://arxiv.org/pdf/2610.24892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4fvkspkpzb4t0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Scalable and Adaptive Distribution Regression via Random Features",
  "title_text": "Scalable and Adaptive Distribution Regression via Random Features",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/4fvkspkpzb4t0",
  "venue": "arXiv",
  "versions": []
}