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

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

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Zhenyu Zhu, Francesco Locatello, Volkan Cevher


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.