{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T16:14:27Z","timestamp":1780416867740,"version":"3.54.1"},"reference-count":22,"publisher":"MIT Press","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p>Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-)metric between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well suited for evaluating graphs that are used for computing interventions. Instead of DAGs, it is also possible to compare CPDAGs, completed partially DAGs that represent Markov equivalence classes. The SID differs significantly from the widely used structural Hamming distance and therefore constitutes a valuable additional measure. We discuss properties of this distance and provide a (reasonably) efficient implementation with software code available on the first author\u2019s home page.<\/jats:p>","DOI":"10.1162\/neco_a_00708","type":"journal-article","created":{"date-parts":[[2015,1,20]],"date-time":"2015-01-20T18:51:10Z","timestamp":1421779870000},"page":"771-799","source":"Crossref","is-referenced-by-count":62,"title":["Structural Intervention Distance for Evaluating Causal Graphs"],"prefix":"10.1162","volume":"27","author":[{"given":"Jonas","family":"Peters","sequence":"first","affiliation":[{"name":"Seminar for Statistics, Department of Mathematics, ETH Z\u00fcrich 8092, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"B\u00fchlmann","sequence":"additional","affiliation":[{"name":"Seminar for Statistics, Department of Mathematics, ETH Z\u00fcrich 8092, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1061"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1031833662"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1260"},{"key":"B4","first-page":"507","volume":"3","author":"Chickering D.","year":"2002","journal-title":"Journal of Machine Learning Research"},{"key":"B5","author":"Claassen T.","year":"2013","journal-title":"Proceedings of the 29th Annual Conference on Uncertainty in Artificial Intelligence"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS940"},{"key":"B7","author":"Coppersmith D.","year":"1987","journal-title":"Proceedings of the 19th Annual ACM Symposium on Theory of Computing"},{"key":"B8","first-page":"443","volume-title":"Recent advances in intelligent information systems","author":"de Jongh M.","year":"2009"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v047.i11"},{"key":"B10","author":"Koller D.","year":"2009","journal-title":"Probabilistic graphical models: Principles and techniques"},{"key":"B11","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522195.001.0001","author":"Lauritzen S.","year":"1996","journal-title":"Graphical models"},{"key":"B13","author":"Meek C.","year":"1995","journal-title":"Proceedings of the 11th Annual Conference on Uncertainty in Artificial Intelligence"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161"},{"key":"B16","author":"Peters J.","year":"2012","journal-title":"Restricted structural equation models for causal inference"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ast043"},{"key":"B18","author":"Ramsey J.","year":"2006","journal-title":"Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1031689015"},{"key":"B20","volume":"2","author":"Shpitser I.","year":"2006","journal-title":"Proceedings of the 21st National Conference on Artificial Intelligence (AAAI)"},{"key":"B21","author":"Shpitser I.","year":"2010","journal-title":"Proceedings of the 26th Annual Conference on Uncertainty in Artificial Intelligence"},{"key":"B22","volume-title":"Causation, prediction, and search","author":"Spirtes P.","year":"2000"},{"key":"B23","author":"Textor J.","year":"2011","journal-title":"Proceedings of the 27th Annual Conference on Uncertainty in Artificial Intelligence"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-006-6889-7"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/NECO_a_00708","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T17:48:58Z","timestamp":1717696138000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/27\/3\/771-799\/8069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["10.1162\/NECO_a_00708"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_00708","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3]]}}}