---
_id: '14953'
abstract:
- lang: eng
  text: This paper provides statistical sample complexity bounds for score-matching
    and its applications in causal discovery. We demonstrate that accurate estimation
    of the score function is achievable by training a standard deep ReLU neural network
    using stochastic gradient descent. We establish bounds on the error rate of recovering
    causal relationships using the score-matching-based causal discovery method of
    Rolland et al. [2022], assuming a sufficiently good estimation of the score function.
    Finally, we analyze the upper bound of score-matching estimation within the score-based
    generative modeling, which has been applied for causal discovery but is also of
    independent interest within the domain of generative models.
acknowledgement: 'We are thankful to the reviewers for providing constructive feedback
  and Kun Zhang and Dominik Janzing for helpful discussion on the special case of
  deterministic children. This work was supported by Hasler Foundation Program: Hasler
  Responsible AI (project number 21043). This work was supported by the Swiss National
  Science Foundation (SNSF) under grant number 200021_205011. Francesco Locatello
  did not contribute to this work at Amazon. '
article_number: '2310.18123'
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhenyu
  full_name: Zhu, Zhenyu
  last_name: Zhu
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
- first_name: Volkan
  full_name: Cevher, Volkan
  last_name: Cevher
citation:
  ama: 'Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching:
    Causal discovery and generative modeling. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2310.18123">10.48550/arXiv.2310.18123</a>'
  apa: 'Zhu, Z., Locatello, F., &#38; Cevher, V. (n.d.). Sample complexity bounds
    for score-matching: Causal discovery and generative modeling. <i>arXiv</i>. <a
    href="https://doi.org/10.48550/arXiv.2310.18123">https://doi.org/10.48550/arXiv.2310.18123</a>'
  chicago: 'Zhu, Zhenyu, Francesco Locatello, and Volkan Cevher. “Sample Complexity
    Bounds for Score-Matching: Causal Discovery and Generative Modeling.” <i>ArXiv</i>,
    n.d. <a href="https://doi.org/10.48550/arXiv.2310.18123">https://doi.org/10.48550/arXiv.2310.18123</a>.'
  ieee: 'Z. Zhu, F. Locatello, and V. Cevher, “Sample complexity bounds for score-matching:
    Causal discovery and generative modeling,” <i>arXiv</i>. .'
  ista: 'Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching:
    Causal discovery and generative modeling. arXiv, 2310.18123.'
  mla: 'Zhu, Zhenyu, et al. “Sample Complexity Bounds for Score-Matching: Causal Discovery
    and Generative Modeling.” <i>ArXiv</i>, 2310.18123, doi:<a href="https://doi.org/10.48550/arXiv.2310.18123">10.48550/arXiv.2310.18123</a>.'
  short: Z. Zhu, F. Locatello, V. Cevher, ArXiv (n.d.).
date_created: 2024-02-07T15:11:11Z
date_published: 2023-10-27T00:00:00Z
date_updated: 2024-02-12T09:45:58Z
day: '27'
department:
- _id: FrLo
doi: 10.48550/arXiv.2310.18123
external_id:
  arxiv:
  - '2310.18123'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2310.18123
month: '10'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: 'Sample complexity bounds for score-matching: Causal discovery and generative
  modeling'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...