Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling
It addresses the need for theoretical guarantees in score-matching methods for researchers in causal inference and generative modeling, though it is incremental as it builds on existing work.
This paper tackles the problem of establishing statistical sample complexity bounds for score-matching in causal discovery and generative modeling, demonstrating that accurate score function estimation is achievable with deep ReLU networks and providing error bounds for causal relationship recovery.
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.