Probabilistic Inference in Hybrid Domains by Weighted Model Integration

Weighted model counting (WMC) on a propositional knowledge base is an effective and general approach to probabilistic inference in a variety of formalisms, includ-ing Bayesian and Markov Networks. However, an in-herent limitation of WMC is that it only admits the in-ference of discrete probability distributions. In this pa-per, we introduce a strict generalization of WMC called weighted model integration that is based on annotating Boolean and arithmetic constraints, and combinations thereof. This methodology is shown to capture discrete, continuous and hybrid Markov networks. We then con-sider the task of parameter learning for a fragment of the language. An empirical evaluation demonstrates the ap-plicability and promise of the proposal.