Learning Weighted Model Integration Distributions

Abstract

Weighted model integration (WMI) is a framework for probabilistic inference over distributions with discrete and continuous variables and structured supports. Despite the growing popularity of WMI, existing density estimators ignore the problem of learning a structured support, and thus fail to handle unfeasible configurations and piecewise-linear relations between continuous variables. We propose lariat, a novel method to tackle this challenging problem. In a first step, our approach induces an SMT(ℒℛA) formula representing the support of the structured distribution. Next, it combines the latter with a density learned using a state-of-the-art estimation method. The overall model automatically accounts for the discontinuous nature of the underlying structured distribution. Our experimental results with synthetic and real-world data highlight the promise of the approach.

Semantic Probabilistic Layers for Neuro-Symbolic Learning

“…This opens up a number of interesting research directions. First, SPLs can be extended to incorporate logical constraints over multiple networks and representable by first-order formulas [45], which we plan to explore in future works, making the circuit construction pipeline totally transparent to users [1] while possibly automatically learning constraints from data [20,47]. Second, we are interested in leveraging SPLs to inject scalable logical constraints into large language models [6] thus equipping them with robust probabilistic reasoning capabilities [29,78].…”

Probabilistic inference using partitioned bayesian networks : introducing a compositional framework

“…WMC has recently been extended to Weighted Model Integration (WMI), which can be used to solve probabilistic reasoning problems that involve both discrete and continuous probability distributions [114]. It is shown that standard knowledge compilation techniques apply to WMI, leading to exact and approximate solvers [60,113]. Based on this finding, we argue that the proposed partitioning technique in this chapter can extend WMI for representations that are less or equally succinct as d-DNNF when dealing with non-linear real arithmetics.…”