Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling
Zhenyu Zhu, Francesco Locatello, Volkan Cevher
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.
BibTeX
@inproceedings{
zhu2023sample,
title={Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling},
author={Zhenyu Zhu and Francesco Locatello and Volkan Cevher},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=uNnPWR66b8}
}