{"type":"ScholarlyArticle","title":"On the Complexity of Counterfactual Reasoning","authors":[{"name":"Yunqiu Han","slug":"yunqiu-han","given":"Yunqiu","family":"Han","affiliation":"University of California , Los Angeles"},{"name":"Yizuo Chen","slug":"yizuo-chen","given":"Yizuo","family":"Chen","affiliation":"University of California , Los Angeles"},{"name":"Adnan Darwiche","slug":"adnan-darwiche","given":"Adnan","family":"Darwiche","affiliation":"University of California , Los Angeles"}],"abstract":"We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks---used in standard counterfactual reasoning that contemplates two worlds, real and imaginary---to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with partially specified SCMs that are coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.","doi":"10.24963/ijcai.2023/630","url":"https://ijcai.org/proceedings/2023/630","pdf":"https://ijcai.org/proceedings/2023/0630.pdf","markdown":"https://ijcai.org/proceedings/2023/630.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/630","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Uncertainty in AI","track":"Main Track","number":630,"pages":{"first":5676,"last":5684},"keywords":["Knowledge Representation and Reasoning: KRR: Causality","Uncertainty in AI: UAI: Bayesian networks","Uncertainty in AI: UAI: Causality, structural causal models and causal inference"],"videos":[],"references":[{"position":1,"raw":"[Avin et al., 2005] Chen Avin, Ilya Shpitser, and Judea Pearl. 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