Assumption violations in causal discovery and the robustness of score matching Advances in Neural Information Processing Systems Montagna, Francesco Mastakouri, Atalanti A. Eulig, Elias Noceti, Nicoletta Rosasco, Lorenzo Janzing, Dominik Aragam, Bryon Locatello, Francesco ; https://orcid.org/0000-0002-4850-0683 ddc:000 When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical properties of their data. Because causal discovery without further assumptions is an ill-posed problem, each algorithm comes with its own set of usually untestable assumptions, some of which are hard to meet in real datasets. Motivated by these considerations, this paper extensively benchmarks the empirical performance of recent causal discovery methods on observational iid data generated under different background conditions, allowing for violations of the critical assumptions required by each selected approach. Our experimental findings show that score matching-based methods demonstrate surprising performance in the false positive and false negative rate of the inferred graph in these challenging scenarios, and we provide theoretical insights into their performance. This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters. Finally, we hope this paper will set a new standard for the evaluation of causal discovery methods and can serve as an accessible entry point for practitioners interested in the field, highlighting the empirical implications of different algorithm choices. Neural Information Processing Systems Foundation 2023 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/14954 https://research-explorer.ista.ac.at/download/14954/22701 Montagna F, Mastakouri AA, Eulig E, et al. Assumption violations in causal discovery and the robustness of score matching. In: <i>37th Conference on Neural Information Processing Systems</i>. Vol 36. Neural Information Processing Systems Foundation; 2023. doi:<a href="https://doi.org/10.52202/075280-2050">10.52202/075280-2050</a> eng info:eu-repo/semantics/altIdentifier/doi/10.52202/075280-2050 info:eu-repo/semantics/altIdentifier/e-issn/1049-5258 info:eu-repo/semantics/altIdentifier/arxiv/2310.13387 info:eu-repo/semantics/openAccess