
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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Efficient SearchBased Weighted Model Integration
Weighted model integration (WMI) extends Weighted model counting (WMC) t...
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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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On the Approximability of Weighted Model Integration on DNF Structures
Weighted model counting admits an FPRAS on DNF structures. We study weig...
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Weighted Model Counting in FO2 with Cardinality Constraints and Counting Quantifiers: A Closed Form Formula
Weighted First Order Model Counting (WFOMC) computes the weighted sum of...
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Scaling up Probabilistic Inference in Linear and NonLinear Hybrid Domains by Leveraging Knowledge Compilation
Weighted model integration (WMI) extends weighted model counting (WMC) i...
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Taming Discrete Integration via the Boon of Dimensionality
Discrete integration is a fundamental problem in computer science that c...
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Measure Theoretic Weighted Model Integration
Weighted model counting (WMC) is a popular framework to perform probabilistic inference with discrete random variables. Recently, WMC has been extended to weighted model integration (WMI) in order to additionally handle continuous variables. At their core, WMI problems consist of computing integrals and sums over weighted logical formulas. From a theoretical standpoint, WMI has been formulated by patching the sum over weighted formulas, which is already present in WMC, with Riemann integration. A more principled approach to integration, which is rooted in measure theory, is Lebesgue integration. Lebesgue integration allows one to treat discrete and continuous variables on equal footing in a principled fashion. We propose a theoretically sound measure theoretic formulation of weighted model integration, which naturally reduces to weighted model counting in the absence of continuous variables. Instead of regarding weighted model integration as an extension of weighted model counting, WMC emerges as a special case of WMI in our formulation.
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