{"type":"ScholarlyArticle","title":"On the Parameterized Complexity of Polytree Learning","authors":[{"name":"Niels Grüttemeier","slug":"niels-gruttemeier","given":"Niels","family":"Grüttemeier","affiliation":""},{"name":"Christian Komusiewicz","slug":"christian-komusiewicz","given":"Christian","family":"Komusiewicz","affiliation":""},{"name":"Nils Morawietz","slug":"nils-morawietz","given":"Nils","family":"Morawietz","affiliation":""}],"abstract":"A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data. Polytree Learning is the problem of learning an optimal Bayesian network that fulfills the additional property that its underlying undirected graph is a forest. In this work, we revisit the complexity of Polytree Learning. We show that Polytree Learning can be solved in single-exponential FPT time for the number of variables. Moreover, we consider the influence of d, the number of variables that might receive a nonempty parent set in the final DAG on the complexity of Polytree Learning. We show that Polytree Learning is presumably not fixed-parameter tractable for d, unlike Bayesian network learning which is fixed-parameter tractable for d. Finally, we show that if d and the maximum parent set size are bounded, then we can obtain efficient algorithms.","doi":"10.24963/ijcai.2021/580","url":"https://ijcai.org/proceedings/2021/580","pdf":"https://ijcai.org/proceedings/2021/0580.pdf","markdown":"https://ijcai.org/proceedings/2021/580.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/580","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Uncertainty in AI","track":"Main Track","number":580,"pages":{"first":4221,"last":4227},"keywords":["Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Uncertainty in AI: Bayesian Networks"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}