Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling

• URL: http://arxiv.org/abs/2310.18123v1
• Date: Fri, 27 Oct 2023 13:09:56 GMT
• Title: Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling
• Authors: Zhenyu Zhu, Francesco Locatello, Volkan Cevher
• Abstract summary: We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method.
• Score: 82.36856860383291
• License: http://creativecommons.org/licenses/by/4.0/
• 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 score-based generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.

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