Hashing-Based Approximate Probabilistic Inference in Hybrid Domains

In recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance 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 partitioned into smaller tasks using universal hashing. An inherent limitation of this approach, however, is that it only admits the inference of discrete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Building on a notion called weighted model integration, 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 evaluations demonstrate the applicability and promise of the proposal.