Sample complexity bounds for score-matching: Causal discovery and generative modeling

preprint Sample complexity bounds for score-matching: Causal discovery and generative modeling submitted Zhenyu Zhu author Francesco Locatello author 26cfd52f-2483-11ee-8040-88983bcc06d40000-0002-4850-0683 Volkan Cevher author FrLo department 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. 2023 eng arXiv 2310.1812310.48550/arXiv.2310.18123 Z. Zhu, F. Locatello, and V. Cevher, “Sample complexity bounds for score-matching: Causal discovery and generative modeling,” arXiv. . Zhu, Zhenyu, Francesco Locatello, and Volkan Cevher. “Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling.” ArXiv, n.d. <a href="https://doi.org/10.48550/arXiv.2310.18123">https://doi.org/10.48550/arXiv.2310.18123</a>. Zhu, Z., Locatello, F., & Cevher, V. (n.d.). Sample complexity bounds for score-matching: Causal discovery and generative modeling. arXiv. <a href="https://doi.org/10.48550/arXiv.2310.18123">https://doi.org/10.48550/arXiv.2310.18123</a> Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching: Causal discovery and generative modeling. arXiv, 2310.18123. Z. Zhu, F. Locatello, V. Cevher, ArXiv (n.d.). Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching: Causal discovery and generative modeling. arXiv. doi:<a href="https://doi.org/10.48550/arXiv.2310.18123">10.48550/arXiv.2310.18123</a> Zhu, Zhenyu, et al. “Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling.” ArXiv, 2310.18123, doi:<a href="https://doi.org/10.48550/arXiv.2310.18123">10.48550/arXiv.2310.18123</a>. 149532024-02-07T15:11:11Z2024-02-12T09:45:58Z