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.

本文提供了得分匹配（Score-Matching）及其在因果发现中的应用的统计样本复杂性界限。我们证明了通过使用随机梯度下降训练标准的深度 ReLU 神经网络可以实现对得分函数的准确估计。我们建立了在得分匹配方法中基于 Rolland 等人 [2022] 的因果发现方法中恢复因果关系的错误率的界限，假设得分函数的估计足够好。最后，我们分析了得分匹配估计在基于得分的生成建模中的上界，这在因果发现领域中既有独立的兴趣，又有独立的生成模型。