{"type":"ScholarlyArticle","title":"Revisiting Causal Discovery from a Complexity-Theoretic Perspective","authors":[{"name":"Robert Ganian","slug":"robert-ganian","given":"Robert","family":"Ganian","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"},{"name":"Viktoriia Korchemna","slug":"viktoriia-korchemna","given":"Viktoriia","family":"Korchemna","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"}],"abstract":"Causal discovery seeks to unveil causal relationships (represented as a so-called causal graph) from observational data. This paper investigates the complex relationship between the graph structure and the efficiency of constraint-based causal discovery algorithms.\r\n    \r\nOur main contributions include (i) a near-tight characterization of which causal graphs admit a small d-separating set for each pair of vertices and thus can potentially be efficiently recovered by a constraint-based causal discovery algorithm, (ii) the explicit construction of a sequence of causal graphs on which the influential PC algorithm might need exponential time, although there is a small d-separating set between every pair of variables, and (iii) the formulation of a new causal discovery algorithm which achieves fixed-parameter running time by considering the maximum number of edge-disjoint paths between variables in the (undirected) super-structure as the parameter. A distinguishing feature of our investigation is that it is carried out within a more fine-grained model which more faithfully captures the infeasibility of performing accurate independence tests for large sets of conditioning variables.","doi":"10.24963/ijcai.2024/374","url":"https://ijcai.org/proceedings/2024/374","pdf":"https://ijcai.org/proceedings/2024/0374.pdf","markdown":"https://ijcai.org/proceedings/2024/374.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/374","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":374,"pages":{"first":3377,"last":3385},"keywords":["Knowledge Representation and Reasoning: KRR: Causality","Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning"],"videos":[],"references":[{"position":1,"raw":"[Chen et al., 2016] Eunice Yuh-Jie Chen, Yujia Shen, Arthur Choi, and Adnan Darwiche. Learning Bayesian networks with ancestral constraints. Advances in Neural Information Processing Systems, 29, 2016.","title":"Learning Bayesian networks with ancestral constraints","authors":"Eunice Yuh-Jie Chen, Yujia Shen, Arthur Choi, Adnan Darwiche","year":"2016","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Claassen et al., 2013] Tom Claassen, Joris M. Mooij, and Tom Heskes. Learning sparse causal models is not NP-hard. CoRR, abs/1309.6824, 2013.","title":"Learning sparse causal models is not NP-hard","authors":"Tom Claassen, M Joris, Tom Mooij, Heskes","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Cygan et al., 2015] Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parame- terized Algorithms. Springer, 2015.","title":"Parameterized Algorithms","authors":"Marek Cygan, V Fedor, Lukasz Fomin, Daniel Kowalik, Dániel Lokshtanov, Marcin Marx, Michal Pilipczuk, Saket Pilipczuk, Saurabh","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Diestel, 2012] Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics. Springer, 2012.","title":"Graph Theory","authors":"Reinhard Diestel","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Downey and Fellows, 2013] Rodney G. Downey and Michael R. Fellows. Fundamentals of parameterized complexity. Texts in Computer Science. Springer Verlag, 2013.","title":"Fundamentals of parameterized complexity","authors":"Rodney G Downey, Michael R Fellows","year":"2013","venue":"Texts in Computer Science","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Eberhardt, 2017] Frederick Eberhardt. Introduction to the foundations of causal discovery. Int. J. Data Sci. Anal., 3(2):81-91, 2017.","title":"Introduction to the foundations of causal discovery","authors":"Frederick Eberhardt","year":"2017","venue":"Int. J. Data Sci. Anal","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Ganian and Korchemna, 2021] Robert Ganian and Viktoriia Korchemna. The complexity of Bayesian network learning: Revisiting the superstructure. In Marc'Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pages 430-442, 2021.","title":"Robert Ganian and Viktoriia Korchemna. The complexity of Bayesian network learning: Revisiting the superstructure","authors":"Korchemna Ganian","year":"2021","venue":"Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Ganian et al., 2022] Robert Ganian, Eun Jung Kim, and Ste- fan Szeider. Algorithmic applications of tree-cut width. SIAM J. Discret. Math., 36(4):2635-2666, 2022.","title":"Algorithmic applications of tree-cut width","authors":"Robert Ganian, Eun Jung Kim, Stefan Szeider","year":"2022","venue":"SIAM J. Discret. Math","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Glymour et al., 2019] Clarc Glymour, Kun Zhang, and Peter Spirtes. Review of causal discovery methods based on graphical models. Frontiers in Genetics, 10:Sec. Statistical Genetics and Methodology, 2019.","title":"Review of causal discovery methods based on graphical models","authors":"Glymour","year":"2019","venue":"Sec. Statistical Genetics and Methodology","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Grüttemeier and Komusiewicz, 2022] Niels Grüttemeier and Christian Komusiewicz. Learning Bayesian networks under sparsity constraints: A parameterized complexity analysis. J. Artif. Intell. Res., 74:1225-1267, 2022.","title":"Niels Grüttemeier and Christian Komusiewicz. Learning Bayesian networks under sparsity constraints: A parameterized complexity analysis","authors":"Komusiewicz Grüttemeier","year":"2022","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Grüttemeier et al., 2021] Niels Grüttemeier, Christian Ko- musiewicz, and Nils Morawietz. On the parameterized complexity of polytree learning. In Zhi-Hua Zhou, editor, Proceedings of the Thirtieth International Joint Confer- ence on Artificial Intelligence, IJCAI 2021, Virtual Event / Montreal, Canada, 19-27 August 2021, pages 4221-4227.","title":"Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. On the parameterized complexity of polytree learning","authors":"Grüttemeier","year":"2021","venue":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Korhonen and Parviainen, 2015] Janne H Korhonen and Pekka Parviainen. Tractable Bayesian network structure learning with bounded vertex cover number. In C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, edi- tors, Advances in Neural Information Processing Systems, volume 28.","title":"Tractable Bayesian network structure learning with bounded vertex cover number","authors":"Parviainen ; ] Korhonen, H Janne, Pekka Korhonen, Parviainen","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"Curran Associates, Inc., 2015.","title":null,"authors":"Curran Associates, Inc","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Mokhtarian et al., 2021] Ehsan Mokhtarian, Sina Akbari, AmirEmad Ghassami, and Negar Kiyavash. A recursive Markov boundary-based approach to causal structure learn- ing. In Thuc Duy Le, Jiuyong Li, Gregory Cooper, Sofia Triantafyllou, Elias Bareinboim, Huan Liu, and Negar Kiyavash, editors, The KDD 2021 Workshop on Causal Discovery, CD@KDD 2021, Singapore, August 15, 2021, volume 150 of Proceedings of Machine Learning Research, pages 26-54. PMLR, 2021.","title":"A recursive Markov boundary-based approach to causal structure learning","authors":"Ehsan Mokhtarian, Sina Akbari, Amiremad Ghassami, Negar Kiyavash","year":"2021","venue":"The KDD 2021 Workshop on Causal Discovery, CD@KDD 2021","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Mokhtarian et al., 2022] Ehsan Mokhtarian, Sina Akbari, Fateme Jamshidi, Jalal Etesami, and Negar Kiyavash. Learning Bayesian networks in the presence of structural side information. In Thirty-Sixth AAAI Conference on Ar- tificial Intelligence, AAAI 2022, Thirty-Fourth Conference on Innovative Applications of Artificial Intelligence, IAAI 2022, The Twelveth Symposium on Educational Advances in Artificial Intelligence, EAAI 2022 Virtual Event, Febru- ary 22 -March 1, 2022, pages 7814-7822. AAAI Press, 2022.","title":"Learning Bayesian networks in the presence of structural side information","authors":"Ehsan Mokhtarian, Sina Akbari, Fateme Jamshidi, Jalal Etesami, Negar Kiyavash","year":"2022","venue":"Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, Thirty-Fourth Conference on Innovative Applications of Artificial Intelligence, IAAI 2022, The Twelveth Symposium on Educational Advances in Artificial Intelligence, EAAI 2022 Virtual Event","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nesetril and de Mendez, 2012] Jaroslav Nesetril and Patrice Ossona de Mendez. Sparsity -Graphs, Struc- tures, and Algorithms, volume 28 of Algorithms and Combinatorics. Springer, 2012.","title":"Jaroslav Nesetril and Patrice Ossona de Mendez","authors":"De Nesetril, Mendez","year":"2012","venue":"Sparsity -Graphs, Structures, and Algorithms","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Ng et al., 2021] Ignavier Ng, Yujia Zheng, Jiji Zhang, and Kun Zhang. Reliable causal discovery with improved exact search and weaker assumptions. In Marc'Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pages 20308-20320, 2021.","title":"Reliable causal discovery with improved exact search and weaker assumptions","authors":"Ng","year":"2021","venue":"Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Niedermeier, 2006] Rolf Niedermeier. Invitation to Fixed- Parameter Algorithms. Oxford Lecture Series in Mathemat- ics and its Applications. Oxford University Press, Oxford, 2006.","title":"Invitation to Fixed-Parameter Algorithms","authors":"Rolf Niedermeier","year":"2006","venue":"Oxford Lecture Series in Mathematics and its Applications","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Ordyniak and Szeider, 2013] Sebastian Ordyniak and Ste- fan Szeider. Parameterized complexity results for exact Bayesian network structure learning. J. Artif. Intell. Res., 46:263-302, 2013.","title":"Sebastian Ordyniak and Stefan Szeider. Parameterized complexity results for exact Bayesian network structure learning","authors":"Szeider Ordyniak","year":"2013","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Perrier et al., 2008] Eric Perrier, Seiya Imoto, and Satoru Miyano. Finding optimal Bayesian network given a super- structure. J. Mach. Learn. Res., 9:2251-2286, 2008.","title":"Finding optimal Bayesian network given a superstructure","authors":"Eric Perrier, Seiya Imoto, Satoru Miyano","year":"2008","venue":"J. Mach. Learn. Res","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Ramaswamy and Szeider, 2022] Vaidyanathan Peruvemba Ramaswamy and Stefan Szeider. Learning large Bayesian networks with expert constraints. In James Cussens and Kun Zhang, editors, 38th Conference on Uncertainty in Artificial Intelligence (UAI 2022), Eindhoven, Netherlands, August 1-5, 2022, Proceedings of Machine Learning Re- search (PMLR), page 180:1592-1601, 2022.","title":"Learning large Bayesian networks with expert constraints","authors":"Peruvemba Vaidyanathan, Stefan Ramaswamy, Szeider","year":"2022","venue":"38th Conference on Uncertainty in Artificial Intelligence (UAI 2022)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Robertson and Seymour, 1986] Neil Robertson and P. D. Seymour. Graph minors. II. Algorithmic aspects of tree- width. J. Algorithms, 7(3):309-322, 1986.","title":"Graph minors. II. Algorithmic aspects of treewidth","authors":"Neil Robertson, P D Seymour","year":"1986","venue":"J. Algorithms","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Shalizi, 2023] Cosma Rohilla Shalizi. Advanced Data Anal- ysis from an Elementary Point of View. Carnegie Mel- lon University, 2023. https://www.stat.cmu.edu/ ∼ cshalizi/ ADAfaEPoV/.","title":"Advanced Data Analysis from an Elementary Point of View","authors":"Cosma Rohilla, Shalizi","year":"2023","venue":null,"doi":null,"url":"https://www.stat.cmu.edu/∼cshalizi/ADAfaEPoV/","internal_url":null},{"position":24,"raw":"[Spirtes et al., 2000] Peter Spirtes, Clark Glymour, and Richard Scheines. Causation, Prediction, and Search, Sec- ond Edition. Adaptive computation and machine learning. MIT Press, 2000.","title":"Causation, Prediction, and Search, Second Edition. Adaptive computation and machine learning","authors":"Peter Spirtes, Clark Glymour, Richard Scheines","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Talvitie and Parviainen, 2020] Topi Talvitie and Pekka Parviainen. Learning Bayesian networks with cops and robbers. In Manfred Jaeger and Thomas Dyhre Nielsen, editors, International Conference on Probabilistic Graphi- cal Models, PGM 2020, 23-25 September 2020, Aalborg, Hotel Comwell Rebild Bakker, Skørping, Denmark, volume 138 of Proceedings of Machine Learning Research, pages 473-484. PMLR, 2020.","title":"Learning Bayesian networks with cops and robbers","authors":"Parviainen Talvitie, Topi Talvitie, Pekka Parviainen","year":"2020","venue":"International Conference on Probabilistic Graphical Models, PGM 2020","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Tian et al., 1998] Jing-Jing Tian, Azaria Paz, and Judea Pearl. Finding minimal D-separators. Technical Report R-254, UCLA, February 1998.","title":"Finding minimal D-separators","authors":"Jing-Jing Tian, Azaria Paz, Judea Pearl","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Tsamardinos et al., 2006] Ioannis Tsamardinos, Laura E. Brown, and Constantin F. Aliferis. The max-min hill- climbing Bayesian network structure learning algorithm. Machine Learning, 65(1):31-78, 2006.","title":"The max-min hillclimbing Bayesian network structure learning algorithm","authors":"Ioannis Tsamardinos, Laura E Brown, Constantin F Aliferis","year":"2006","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Wienöbst and Liskiewicz, 2021] Marcel Wienöbst and Ma- ciej Liskiewicz. An approach to reduce the number of conditional independence tests in the PC algorithm. In Stefan Edelkamp, Ralf Möller, and Elmar Rueckert, editors, KI 2021: Advances in Artificial Intelligence -44th German Conference on AI, Virtual Event, September 27 -October 1, 2021, Proceedings, volume 12873 of Lecture Notes in Computer Science, pages 276-288. Springer, 2021.","title":"Marcel Wienöbst and Maciej Liskiewicz. An approach to reduce the number of conditional independence tests in the PC algorithm","authors":"Liskiewicz Wienöbst","year":"2021","venue":"Advances in Artificial Intelligence -44th German Conference on AI, Virtual Event","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}