{
  "abstract": "Sparse Gaussian processes achieve $O(N)$ inference by replacing the kernel with an appropriate expansion in a fixed basis $\\{ϕ_j\\}$ on the input space. Given a compute budget $M \\ll N$, practitioners conventionally truncate the basis to its first $M$ entries. Nothing in the formalism, however, prevents one from selecting only those $M$ basis functions that matter for the data at hand. This would avoid spending budget on basis functions where there is no signal, but it requires a criterion for ranking the candidates. We propose three such criteria derived from an information-theoretic view of the basis-function selection problem. Each criterion matches a different state of knowledge at selection time: a no-data state, a no-prior state, and an in-between state. We then study the performance of truncation versus selection strategies on six UCI regression benchmarks across three basis families: Hilbert-space Gaussian processes (HSGP), variational Fourier features (VFF), and variational inducing spherical harmonics (VISH). We observe that the no-data criterion is a safe default, matching or improving on truncation for HSGP, VFF and VISH, with substantial gains for VISH and improvements over a recently developed selection heuristic for that basis family. The data-aware no-prior and in-between criteria provide substantial gains over truncation specifically for HSGP, which is the most broadly used of the three families in practice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26624",
  "author_total": 2,
  "authors": [
    {
      "name": "Marnix Van Soom"
    },
    {
      "name": "Ivan De Boi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e25eqzvz9988z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26624",
  "fulltext_url": null,
  "id": "e25eqzvz9988z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26624",
  "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|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214077578",
  "pdf_url": "https://arxiv.org/pdf/2609.26624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e25eqzvz9988z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.26624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26624"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "On Basis Function Selection for Sparse Gaussian Process Regression",
  "title_text": "On Basis Function Selection for Sparse Gaussian Process Regression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/e25eqzvz9988z",
  "venue": "arXiv",
  "versions": []
}