  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.
