Sample complexity bounds for score-matching: Causal discovery and generative modeling
Zhu Z, Locatello F, Cevher V. 2023. Sample complexity bounds for score-matching: Causal discovery and generative modeling. 37th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 36, 3325–3337.
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Author
Zhu, Zhenyu;
Locatello, FrancescoISTA 
;
Cevher, Volkan
;
Cevher, VolkanCorresponding author has ISTA affiliation
Department
Series Title
Advances in Neural Information Processing Systems
Abstract
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 scorebased generative modeling, which has been applied for causal discovery but is also
of independent interest within the domain of generative models.y
Publishing Year
Date Published
2023-10-27
Proceedings Title
37th Conference on Neural Information Processing Systems
Publisher
Neural Information Processing Systems Foundation
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.
Volume
36
Page
3325-3337
Conference
NeurIPS: Neural Information Processing Systems
Conference Location
New Orleans, LO, United States
Conference Date
2023-12-12 – 2023-12-16
ISBN
eISSN
IST-REx-ID
Cite this
Zhu Z, Locatello F, Cevher V. Sample complexity bounds for score-matching: Causal discovery and generative modeling. In: 37th Conference on Neural Information Processing Systems. Vol 36. Neural Information Processing Systems Foundation; 2023:3325-3337. doi:10.52202/075280-0147
Zhu, Z., Locatello, F., & Cevher, V. (2023). Sample complexity bounds for score-matching: Causal discovery and generative modeling. In 37th Conference on Neural Information Processing Systems (Vol. 36, pp. 3325–3337). New Orleans, LO, United States: Neural Information Processing Systems Foundation. https://doi.org/10.52202/075280-0147
Zhu, Zhenyu, Francesco Locatello, and Volkan Cevher. “Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling.” In 37th Conference on Neural Information Processing Systems, 36:3325–37. Neural Information Processing Systems Foundation, 2023. https://doi.org/10.52202/075280-0147.
Z. Zhu, F. Locatello, and V. Cevher, “Sample complexity bounds for score-matching: Causal discovery and generative modeling,” in 37th Conference on Neural Information Processing Systems, New Orleans, LO, United States, 2023, vol. 36, pp. 3325–3337.
Zhu Z, Locatello F, Cevher V. 2023. Sample complexity bounds for score-matching: Causal discovery and generative modeling. 37th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 36, 3325–3337.
Zhu, Zhenyu, et al. “Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling.” 37th Conference on Neural Information Processing Systems, vol. 36, Neural Information Processing Systems Foundation, 2023, pp. 3325–37, doi:10.52202/075280-0147.
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