Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models

This research paper explores using score matching—a technique for estimating the gradient of a data distribution's logarithm—to perform causal discovery in nonlinear additive noise models. The authors demonstrate that the causal graph's structure can be inferred from the score function, particularly its Jacobian. They propose a new algorithm, SCORE, which estimates the causal order by analyzing the variance of the score's Jacobian diagonal elements and then prunes edges using established methods like CAM. Empirical results on synthetic and real-world datasets indicate that SCORE is competitive with existing causal discovery methods while being significantly faster, and it shows robustness to non-Gaussian noise.