The finite model theory of Bayesian networks: Descriptive complexity

© 2018 International Joint Conferences on Artificial Intelligence.All right reserved. We adapt the theory of descriptive complexity to encompass Bayesian networks, so as to quantify the expressivity of Bayesian network specifications based on predicates and quantifiers. We show that Bayesian network specifications that employ first-order quantification capture the complexity class PP; by allowing quantification over predicates, the resulting Bayesian network specifications capture each class in the hierarchy PPNP...NP , a result that does not seem to have equivalent in the literature.