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In many domains, worst-case guarantees on the performance (e.g., predictionaccuracy) of a decision function subject to distributional shifts anduncertainty about the environment are crucial. In this work we develop a methodto quantify the robustness of decision functions with respect to credalBayesian networks, formal parametric models of the environment whereuncertainty 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 faithfullytransfer the problem into a constrained optimization problem on a probabilisticcircuit. By performing a simple constraint relaxation, we show how to obtain aguaranteed upper bound on MARmax in linear time in the size of the circuit. Wefurther theoretically characterize this constraint relaxation in terms of theoriginal Bayesian network structure, which yields insight into the tightness ofthe bound. We implement the method and provide experimental evidence that theupper bound is often near tight and demonstrates improved scalability comparedto other methods.

Robustness Guarantees for Credal Bayesian Networks via Constraint Relaxation over Probabilistic Circuits