Efficient Symbolic Integration for Probabilistic Inference

Kolb, Samuel; Mladenov, Martin; Sanner, Scott; Belle, Vaishak; Kersting, Kristian

doi:10.24963/ijcai.2018/698

Cited by 13 publications

(21 citation statements)

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“…In Q3 we compare Symbo to the existing WMI solver of (Morettin, Passerini, and Sebastiani 2017), which uses predicate abstraction, SMT solving and numerical integration, and to the solver of (Kolb et al 2018), which uses XADDs (Sanner and Abbasnejad 2012) and hence symbolic integration.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…By allowing Symbo to handle also bounded polynomial weights, instead of probability density distributions, we can compare Symbo to the existing exact WMI solvers of WMI-PA (Morettin, Passerini, and Sebastiani 2017) and WMI-XADD (Kolb et al 2018). This extension of Symbo is necessary as these solvers are limited to polynomial weights and cannot handle proper probability densities.…”

Section: Q3 (Wmi)mentioning

confidence: 99%

“…As seen in section 6, WMI has also been studied in the context of XADDs (Kolb et al 2018) and the approach is closely related to Symbo. Here again, the weight functions considered are only of polynomial form.…”

Section: Related Workmentioning

confidence: 99%

“…To repair this omission, WMC has recently been extended towards weighted model integration (WMI) (Belle, Passerini, and Van den Broeck 2015), supporting additionally continuous variables. However, the weight functions supported within current formulations of WMI (Belle, Passerini, and Van den Broeck 2015;Belle et al 2016;Morettin, Passerini, and Sebastiani 2017;Kolb et al 2018) allow only for piecewise polynomial functions. Moreover, none of these prior works has studied the applicability of knowledge compilation to WMI.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

Martires

Dries

Raedt

2019

AAAI

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Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

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Section: Experimental Evaluationmentioning

confidence: 99%

Section: Q3 (Wmi)mentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

Martires

Dries

Raedt

2019

AAAI

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“…We were unable to compare the performance with the framework developed in[25] owing to compatibility issues in the experimental setup. Since it is reported to perform comparably to[29], all comparisons made in this paper are in reference to the pipeline developed in[29].…”

mentioning

confidence: 99%

Scaling up Probabilistic Inference in Linear and Non-linear Hybrid Domains by Leveraging Knowledge Compilation

Fuxjaeger

Belle

2020

Proceedings of the 12th International Conference on Agents and Artificial Intelligence

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Weighted model integration (WMI) extends weighted model counting (WMC) in providing a computational abstraction for probabilistic inference in mixed discrete-continuous domains. WMC has emerged as an assembly language for state-of-the-art reasoning in Bayesian networks, factor graphs, probabilistic programs and probabilistic databases.In this regard, WMI shows immense promise to be much more widely applicable, especially as many real-world applications involve attribute and feature spaces that are continuous and mixed. Nonetheless, state-of-the-art tools for WMI are limited and less mature than their propositional counterparts.In this work, we propose a new implementation regime that leverages propositional knowledge compilation for scaling up inference. In particular, we use sentential decision diagrams, a tractable representation of Boolean functions, as the underlying model counting and model enumeration scheme. Our regime performs competitively to state-of-theart WMI systems, but is also shown, for the first time, to handle non-linear constraints over non-linear potentials.

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Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Belle

2020

Lecture Notes in Computer Science

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The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains.

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Efficient Symbolic Integration for Probabilistic Inference

Cited by 13 publications

References 0 publications

Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

Scaling up Probabilistic Inference in Linear and Non-linear Hybrid Domains by Leveraging Knowledge Compilation

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

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