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In particular, we focus on approaches for learning directed acyclic graphs and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of <jats:italic>equivalence classes<\/jats:italic> over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding <jats:italic>interventional<\/jats:italic> data.<\/jats:p>","DOI":"10.1007\/s10208-022-09581-9","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T19:02:40Z","timestamp":1659380560000},"page":"1781-1815","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Causal Structure Learning: A Combinatorial Perspective"],"prefix":"10.1007","volume":"23","author":[{"given":"Chandler","family":"Squires","sequence":"first","affiliation":[]},{"given":"Caroline","family":"Uhler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,1]]},"reference":[{"key":"9581_CR1","unstructured":"Acharya, J., Bhattacharyya, A., Daskalakis, C., Kandasamy, S.: Learning and testing causal models with interventions. 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