Abstract
Weighted model integration (WMI) is a framework to perform advanced probabilistic inference in hybrid domains, i.e., on distributions over mixed continuous-discrete random variables and in the presence of complex logical and arithmetic constraints. It generalizes weighted model counting from propositional logic to Satisfiability Modulo Theory. In this talk, I will briefly describe some of the existing WMI solvers. Further, I will talk about tractability analysis on the WMI problem classes, that characterize the complexity using primal graphs with treewidth and diameter and discover the largest tractable WMI problem class so far. Finally, I will show one of the applications of WMI in Bayesian deep learning to build accurate uncertainty estimation algorithms.