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.

翻译：本文给出了分数匹配及其在因果发现中应用的统计样本复杂度界。我们证明了通过使用随机梯度下降训练标准深度ReLU神经网络可以实现对分数函数的准确估计。在假设分数函数估计足够好的前提下，我们建立了基于Rolland等人[2022]的分数匹配因果发现方法恢复因果关系误差率的界。最后，我们分析了分数匹配估计在基于分数的生成建模中的上界，该方法虽已应用于因果发现，但在生成模型领域也具有独立的研究价值。