How to Exploit Structure while Solving Weighted Model Integration Problems
Conference on Uncertainty in Artificial Intelligence
Weighted model counting (WMC) is a stateof-the-art technique for probabilistic inference in discrete domains. WMC has recently been extended towards weighted model integration (WMI) in order to handle discrete and continuous distributions alike. While a number of WMI solvers have been introduced, their relationships, strengths and weaknesses are not yet well understood. WMI solving consists of two sub-problems: 1) finding convex polytopes; and 2) integrating over them efficiently. We formalize
... he first step as λ-SMT and discuss what strategies solvers apply to solve both the λ-SMT and the integration problem. This formalization allows us to compare state-of-the-art solvers and their behaviour across different types of WMI problems. Moreover, we identify factorizability of WMI problems as a key property that emerges in the context of probabilistic programming. Problems that can be factorized can be solved more efficiently. However, current solvers exploiting this property restrict themselves to WMI problems with univariate conditions and fully factorizable weight functions. We introduce a new algorithm, F-XSDD, that lifts these restrictions and can exploit factorizability in WMI problems with multivariate conditions and partially factorizable weight functions. Through an empirical evaluation, we show the effectiveness of our approach.