Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Abstract

Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing techniques for hybrid probabilistic inference with logic and algebraic constraints. We leverage weighted model integration as a unifying formalism and discuss the different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative overview of existing implementations and a critical discussion of open challenges and promising research directions.

Inference and Learning with Model Uncertainty in Probabilistic Logic Programs

“…Under specific conditions, calculating higher order moments can be done in polynomial time as well, as shown by Khosravi et al (2019). More general computations, referred to as weighted model integration (Belle, Passerini, and Van den Broeck 2015; Morettin et al 2021), are known to be #P-hard even with the circuit given (Zuidberg Dos Martires, Dries, and De Raedt 2019).…”