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

Martires, Pedro Zuidberg Dos; Dries, Anton; Raedt, Luc De

doi:10.1609/aaai.v33i01.33017825

Cited by 17 publications

(13 citation statements)

References 19 publications

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“…However, little attention has been given to the design of algorithms for structure learning of hybrid SRL models. The same is true for works on hybrid probabilistic programming (HProbLog, Gutmann et al 2010), (DC, Gutmann et al 2011;Nitti et al 2016a), (Extended-Prism, Islam et al 2012), (Hybrid-cplint, Alberti et al 2017), (Michels et al 2016), (BLOG, Wu et al 2018), (Dos Martires et al 2019). Closest to our work is the work on hybrid relational dependency networks (HRDNs, Ravkic et al 2015), for which structure learning was also studied, but this learning algorithm assumes that the data is fully observed.…”

Section: Introductionmentioning

confidence: 89%

Learning Distributional Programs for Relational Autocompletion

Kumar

Kuželka

Raedt

2021

Theory and Practice of Logic Programming

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Relational autocompletion is the problem of automatically filling out some missing values in multi-relational data. We tackle this problem within the probabilistic logic programming framework of Distributional Clauses (DCs), which supports both discrete and continuous probability distributions. Within this framework, we introduce DiceML – an approach to learn both the structure and the parameters of DC programs from relational data (with possibly missing data). To realize this, DiceML integrates statistical modeling and DCs with rule learning. The distinguishing features of DiceML are that it (1) tackles autocompletion in relational data, (2) learns DCs extended with statistical models, (3) deals with both discrete and continuous distributions, (4) can exploit background knowledge, and (5) uses an expectation–maximization-based (EM) algorithm to cope with missing data. The empirical results show the promise of the approach, even when there is missing data.

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Section: Introductionmentioning

confidence: 89%

Learning Distributional Programs for Relational Autocompletion

Kumar

Kuželka

Raedt

2021

Theory and Practice of Logic Programming

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“…Unfortunately, however, by giving up the propositional language, and in particular, the use of arithmetic circuits, we loose the tractability results and unified evaluation scheme offered by AMC. As mentioned, in limited settings, continuous properties can nonetheless be accorded to the atomic propositions, as considered in [40,84].…”

Section: Statistical Modelingmentioning

confidence: 99%

“…The main limitation of the AMC proposal is that the underlying language is propositional logic, and so the semantics is that of classical logic and computations are essentially defined over discrete spaces. It is, however, possible to accord continuous properties to the underlying propositions [84], which may be sufficient in some cases, but it does not allow for arbitrary arithmetical reasoning. So, the AMC proposal offers an attractive generic inference scheme in the propositional setting.…”

Section: Introductionmentioning

confidence: 99%

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Semiring programming: A semantic framework for generalized sum product problems

Belle

Raedt

2020

International Journal of Approximate Reasoning

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To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this.In an attempt to alleviate this situation, we position and motivate a new declarative programming framework in this paper. We focus on the semantical foundations in service of providing abstractions of well-known problems such as SAT, Bayesian inference, generative models, learning and convex optimization. Programs are understood in terms of first-order logic structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines and represent non-standard problems over unbounded domains. Thus, the main thrust of this paper is to view such well-known problems through a unified lens in the hope that appropriate solver strategies (exact, approximate, portfolio or hybrid) may emerge that tackle real-world problems in a principled way.

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“…WMC is one of the state-of-the-art approaches for inference in many discrete probabilistic models. Existing general techniques for exact WMI include DPLL-based search with numerical [3,25,26] or symbolic integration [12] and compilation-based algorithms [19,32].…”

Section: Related Workmentioning

confidence: 99%

Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing

Zeng,

Yan,

Morettin

et al. 2019

Preprint

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Weighted model integration (WMI) is a very appealing framework for probabilistic inference: it allows to express the complex dependencies of real-world 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 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 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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Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

Cited by 17 publications

References 19 publications

Learning Distributional Programs for Relational Autocompletion

Learning Distributional Programs for Relational Autocompletion

Semiring programming: A semantic framework for generalized sum product problems

Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing

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