{
  "abstract": "We introduce the Functional Spectral-Newton Method (FSNM) for learning the leading singular structure of a conditional expectation operator without fixing a basis or reproducing kernel Hilbert space. FSNM fits a low-rank representation of the centered joint-to-product density ratio kernel by alternating functional Newton updates. Each update reduces to a preconditioned regression, which we approximate with vector-valued regression trees in a stagewise boosting procedure. At the population level, we establish descent and an $O(1/T)$ best-iterate block-stationarity rate under a relative weak-learner accuracy condition, and show that every nondegenerate local minimum over the full centered $L^2$ spaces is a globally optimal rank-$d$ approximation. Synthetic experiments show that FSNM recovers a low-rank density ratio and its leading spectral structure, and that the same learned kernel can answer multiple conditional queries without refitting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35598",
  "author_total": 4,
  "authors": [
    {
      "name": "Thiago Ramos"
    },
    {
      "name": "Alek Fröhlich"
    },
    {
      "name": "Daniel Perazzo"
    },
    {
      "name": "Massimiliano Pontil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82sd4mwkd0g3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35598",
  "fulltext_url": null,
  "id": "82sd4mwkd0g3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35598",
  "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": "W7214764435",
  "pdf_url": "https://arxiv.org/pdf/2609.35598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82sd4mwkd0g3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.35598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35598"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Learning Conditional Expectation Operators via Functional Newton Updates",
  "title_text": "Learning Conditional Expectation Operators via Functional Newton Updates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/82sd4mwkd0g3b",
  "venue": "arXiv",
  "versions": []
}