{"oa":1,"oa_version":"Preprint","date_created":"2024-02-07T15:11:11Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","title":"Sample complexity bounds for score-matching: Causal discovery and generative modeling","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. ","status":"public","type":"preprint","doi":"10.48550/arXiv.2310.18123","author":[{"full_name":"Zhu, Zhenyu","last_name":"Zhu","first_name":"Zhenyu"},{"orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","last_name":"Locatello"},{"full_name":"Cevher, Volkan","last_name":"Cevher","first_name":"Volkan"}],"day":"27","publication":"arXiv","external_id":{"arxiv":["2310.18123"]},"article_processing_charge":"No","month":"10","date_updated":"2024-02-12T09:45:58Z","publication_status":"submitted","date_published":"2023-10-27T00:00:00Z","citation":{"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>.","ieee":"Z. Zhu, F. Locatello, and V. Cevher, “Sample complexity bounds for score-matching: Causal discovery and generative modeling,” <i>arXiv</i>. .","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>","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>.","ista":"Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching: Causal discovery and generative modeling. arXiv, 2310.18123.","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>","short":"Z. Zhu, F. Locatello, V. Cevher, ArXiv (n.d.)."},"language":[{"iso":"eng"}],"department":[{"_id":"FrLo"}],"article_number":"2310.18123","_id":"14953","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.18123","open_access":"1"}],"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."}]}