Hashing-Based Approximate Probabilistic Inference in Hybrid Domains

In recent years, there has been considerable progress on fast randomized algorithms that ap-proximate probabilistic inference with tight toler-ance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be parti-tioned into smaller tasks using universal hashing. An inherent limitation of this approach, how-ever, is that it only admits the inference of dis-crete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Build-ing on a notion called weighted model integra-tion, which is a strict generalization of WMC and is based on annotating Boolean and arithmetic constraints, we show how probabilistic inference in hybrid domains can be put within reach of hashing-based WMC solvers. Empirical evalu-ations demonstrate the applicability and promise of the proposal.