
Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing
Weighted model integration (WMI) is a very appealing framework for proba...
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Policy Message Passing: A New Algorithm for Probabilistic Graph Inference
A general graphstructured neural network architecture operates on graph...
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Knowledge Compilation with Continuous Random Variables and its Application in Hybrid Probabilistic Logic Programming
In probabilistic reasoning, the traditionally discrete domain has been e...
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Replicated Vector Approximate Message Passing For Resampling Problem
Resampling techniques are widely used in statistical inference and ensem...
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Lifted Hybrid Variational Inference
A variety of lifted inference algorithms, which exploit model symmetry t...
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Efficient SearchBased Weighted Model Integration
Weighted model integration (WMI) extends Weighted model counting (WMC) t...
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Strudel: Learning StructuredDecomposable Probabilistic Circuits
Probabilistic circuits (PCs) represent a probability distribution as a c...
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Hybrid Probabilistic Inference with Logical Constraints: Tractability and MessagePassing
Weighted model integration (WMI) is a very appealing framework for probabilistic inference: it allows to express the complex dependencies of realworld hybrid scenarios where variables are heterogeneous in nature (both continuous and discrete) via the language of Satisfiability Modulo Theories (SMT); as well as computing probabilistic queries with arbitrarily complex logical constraints. Recent work has shown WMI inference to be reducible to a model integration (MI) problem, under some assumptions, thus effectively allowing hybrid probabilistic reasoning by volume computations. In this paper, we introduce a novel formulation of MI via a message passing scheme that allows to efficiently compute the marginal densities and statistical moments of all the variables in linear time. As such, we are able to amortize inference for arbitrarily rich MI queries when they conform to the problem structure, here represented as the primal graph associated to the SMT formula. Furthermore, we theoretically trace the tractability boundaries of exact MI. Indeed, we prove that in terms of the structural requirements on the primal graph that make our MI algorithm tractable  bounding its diameter and treewidth  the bounds are not only sufficient, but necessary for tractable inference via MI.
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