
Hybrid Probabilistic Inference with Logical Constraints: Tractability and MessagePassing
Weighted model integration (WMI) is a very appealing framework for proba...
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Approximate Counting in SMT and Value Estimation for Probabilistic Programs
#SMT, or model counting for logical theories, is a wellknown hard probl...
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Message passing for quantified Boolean formulas
We introduce two types of message passing algorithms for quantified Bool...
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Hybrid SRL with Optimization Modulo Theories
Generally speaking, the goal of constructive learning could be seen as, ...
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Monte Carlo AntiDifferentiation for Approximate Weighted Model Integration
Probabilistic inference in the hybrid domain, i.e. inference over discre...
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Efficient SearchBased Weighted Model Integration
Weighted model integration (WMI) extends Weighted model counting (WMC) t...
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SemanticallyAligned Universal TreeStructured Solver for Math Word Problems
A practical automatic textual math word problems (MWPs) solver should be...
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Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing
Weighted model integration (WMI) is a very appealing framework for probabilistic inference: it allows to express the complex dependencies of realworld problems where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem at all, or they are limited to too restrictive structures. To narrow this gap, we derive a factorized formalism of WMI enabling us to devise a scalable WMI solver based on message passing, MPWMI. Namely, MPWMI is the first WMI solver which allows to: 1) perform exact inference on the full class of treestructured WMI problems; 2) compute all marginal densities in linear time; 3) amortize inference inter query. Experimental results show that our solver dramatically outperforms the existing WMI solvers on a large set of benchmarks.
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