{"type":"ScholarlyArticle","title":"Robustness Guarantees for Credal Bayesian Networks via Constraint Relaxation over Probabilistic Circuits","authors":[{"name":"Hjalmar Wijk","slug":"hjalmar-wijk","given":"Hjalmar","family":"Wijk","affiliation":"University of Oxford"},{"name":"Benjie Wang","slug":"benjie-wang","given":"Benjie","family":"Wang","affiliation":"University of Oxford"},{"name":"Marta Kwiatkowska","slug":"marta-kwiatkowska","given":"Marta","family":"Kwiatkowska","affiliation":"University of Oxford"}],"abstract":"In many domains, worst-case guarantees on the performance (e.g. prediction accuracy) of a decision function subject to distributional shifts and uncertainty about the environment are crucial. In this work we develop a method to quantify the robustness of decision functions with respect to credal Bayesian networks, formal parametric models of the environment where uncertainty is expressed through credal sets on the parameters. In particular, we address the maximum marginal probability (MARmax) problem, that is, determining the greatest probability of an event (such as misclassification) obtainable for parameters in the credal set. We develop a method to faithfully transfer the problem into a constrained optimization problem on a probabilistic circuit. By performing a simple constraint relaxation, we show how to obtain a guaranteed upper bound on MARmax in linear time in the size of the circuit. We further theoretically characterize this constraint relaxation in terms of the original Bayesian network structure, which yields insight into the tightness of the bound. We implement the method and provide experimental evidence that the upper bound is often near tight and demonstrates improved scalability compared to other methods.","doi":"10.24963/ijcai.2022/677","url":"https://ijcai.org/proceedings/2022/677","pdf":"https://ijcai.org/proceedings/2022/0677.pdf","markdown":"https://ijcai.org/proceedings/2022/677.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/677","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Uncertainty in AI","track":"Main Track","number":677,"pages":{"first":4885,"last":4892},"keywords":["Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis","AI Ethics, Trust, Fairness: Safety & Robustness","Uncertainty in AI: Bayesian Networks","Constraint Satisfaction and Optimization: Constraint Satisfaction","Uncertainty in AI: Tractable Probabilistic Models"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986933","length_sec":70,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985076","length_sec":337,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Antonucci et al., 2010] Alessandro Antonucci, Yi Sun, Cas- sio P. de Campos, and Marco Zaffalon. 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