{"_id":"21066","ddc":["000"],"arxiv":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"552-605","main_file_link":[{"open_access":"1","url":"https://proceedings.mlr.press/v275/montagna25a.html"}],"file":[{"file_size":1739334,"relation":"main_file","checksum":"f2bc44b2320667d4049b3518b1f2fe5d","file_name":"montagna25a.pdf","success":1,"access_level":"open_access","creator":"flocatel","date_created":"2026-01-29T14:17:48Z","content_type":"application/pdf","file_id":"21067","date_updated":"2026-01-29T14:17:48Z"}],"citation":{"mla":"Montagna, Francesco, et al. “Score Matching through the Roof: Linear, Nonlinear, and Latent Variables Causal Discovery.” <i>Proceedings of the Fourth Conference on Causal Learning and Reasoning</i>, vol. 275, ML Research Press, 2025, pp. 552–605.","ama":"Montagna F, Faller P, Blöbaum P, Kirschbaum E, Locatello F. Score matching through the roof: Linear, nonlinear, and latent variables causal discovery. In: <i>Proceedings of the Fourth Conference on Causal Learning and Reasoning</i>. Vol 275. ML Research Press; 2025:552-605.","short":"F. Montagna, P. Faller, P. Blöbaum, E. Kirschbaum, F. Locatello, in:, Proceedings of the Fourth Conference on Causal Learning and Reasoning, ML Research Press, 2025, pp. 552–605.","chicago":"Montagna, Francesco, Philipp Faller, Patrik Blöbaum, Elke Kirschbaum, and Francesco Locatello. “Score Matching through the Roof: Linear, Nonlinear, and Latent Variables Causal Discovery.” In <i>Proceedings of the Fourth Conference on Causal Learning and Reasoning</i>, 275:552–605. ML Research Press, 2025.","apa":"Montagna, F., Faller, P., Blöbaum, P., Kirschbaum, E., &#38; Locatello, F. (2025). Score matching through the roof: Linear, nonlinear, and latent variables causal discovery. In <i>Proceedings of the Fourth Conference on Causal Learning and Reasoning</i> (Vol. 275, pp. 552–605). Lausanne, Switzerland: ML Research Press.","ista":"Montagna F, Faller P, Blöbaum P, Kirschbaum E, Locatello F. 2025. Score matching through the roof: Linear, nonlinear, and latent variables causal discovery. Proceedings of the Fourth Conference on Causal Learning and Reasoning. CLeaR: Conference on Causal Learning and Reasoning, PMLR, vol. 275, 552–605.","ieee":"F. Montagna, P. Faller, P. Blöbaum, E. Kirschbaum, and F. Locatello, “Score matching through the roof: Linear, nonlinear, and latent variables causal discovery,” in <i>Proceedings of the Fourth Conference on Causal Learning and Reasoning</i>, Lausanne, Switzerland, 2025, vol. 275, pp. 552–605."},"OA_place":"publisher","OA_type":"gold","abstract":[{"lang":"eng","text":"Causal discovery from observational data holds great promise, but existing methods rely on strong assumptions about the underlying causal structure, often requiring full observability of all relevant variables. We tackle these challenges by leveraging the score function ∇logp(X)\r\n of observed variables for causal discovery and propose the following contributions. First, we generalize the existing results of identifiability with the score to additive noise models with minimal requirements on the causal mechanisms. Second, we establish conditions for inferring causal relations from the score even in the presence of hidden variables; this result is two-faced: we demonstrate the score’s potential as an alternative to conditional independence tests to infer the equivalence class of causal graphs with hidden variables, and we provide the necessary conditions for identifying direct causes in latent variable models. Building on these insights, we propose a flexible algorithm for causal discovery across linear, nonlinear, and latent variable models, which we empirically validate."}],"quality_controlled":"1","status":"public","file_date_updated":"2026-01-29T14:17:48Z","date_published":"2025-05-01T00:00:00Z","acknowledgement":"Philipp M. Faller was supported by a doctoral scholarship of the Studienstiftung des deutschen\r\nVolkes (German Academic Scholarship Foundation). This work has been supported by AFOSR,\r\ngrant n. FA8655-20-1-7035. FM is supported by Programma Operativo Nazionale ricerca e innovazione 2014-2020. We thank Atalanti A. Mastakouri, Kun Zhang and Haoyue Dai for the insightful discussions.","oa":1,"license":"https://creativecommons.org/licenses/by/4.0/","language":[{"iso":"eng"}],"title":"Score matching through the roof: Linear, nonlinear, and latent variables causal discovery","month":"05","type":"conference","publication":"Proceedings of the Fourth Conference on Causal Learning and Reasoning","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       275","day":"01","author":[{"full_name":"Montagna, Francesco","first_name":"Francesco","last_name":"Montagna"},{"full_name":"Faller, Philipp","last_name":"Faller","first_name":"Philipp"},{"first_name":"Patrik","last_name":"Blöbaum","full_name":"Blöbaum, Patrik"},{"full_name":"Kirschbaum, Elke","last_name":"Kirschbaum","first_name":"Elke"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","orcid":"0000-0002-4850-0683","last_name":"Locatello","first_name":"Francesco","full_name":"Locatello, Francesco"}],"publication_status":"published","publication_identifier":{"eissn":["2640-3498"]},"date_created":"2026-01-29T14:19:09Z","conference":{"start_date":"2025-05-07","location":"Lausanne, Switzerland","end_date":"2025-05-09","name":"CLeaR: Conference on Causal Learning and Reasoning"},"date_updated":"2026-02-10T11:54:02Z","department":[{"_id":"FrLo"}],"volume":275,"alternative_title":["PMLR"],"external_id":{"arxiv":["2407.18755"]},"publisher":"ML Research Press","corr_author":"1","oa_version":"Published Version","has_accepted_license":"1","year":"2025"}