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Scalable Causal Discovery with Score Matching
Francesco Montagna · Nicoletta Noceti · Lorenzo Rosasco · Kun Zhang · Francesco Locatello

This paper demonstrates how to discover the whole causal graph from the second derivative of the log-likelihood in observational non-linear additive Gaussian noise models. Leveraging scalable machine learning approaches to approximate the score function $\nabla \operatorname{log}p(\mathbf{X})$, we extend the work of Rolland et al., 2022, that only recovers the topological order from the score and requires an expensive pruning step to discover the edges.Our analysis leads to DAS, a practical algorithm that reduces the complexity of the pruning by a factor proportional to the graph size. In practice, DAS achieves competitive accuracy with current state-of-the-art while being over an order of magnitude faster. Overall, our approach enables principled and scalable causal discovery, significantly lowering the compute bar.

#### Author Information

##### Francesco Montagna (University of Genoa)

I am a PhD student jointly between University of Genova and Amazon AWS Tuebingen. I am co-supervised by professors Lorenzo Rosasco and Nicoletta Noceti from University of Genoa, and Dr. Francesco Locatello drom Amazon AWS. I am doing a research internship at Amazon AWS Tuebingen until April 2023