Lifted Junction Tree Algorithm

Braun, Tanya; Möller, Ralf

doi:10.1007/978-3-319-46073-4_3

Cited by 32 publications

(6 citation statements)

References 6 publications

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“…This work follows a long line of research in lifted inference on statistical-relational models. Many such papers have focused on operating on first-order versions of graphical models directly (Poole 2003;Milch et al 2008;Taghipour et al 2013;Braun and Möller 2016). On the other hand, a separate line of work has introduced WFOMC as a natural extension of its propositional counterpart WMC, and has shown how inference in the first-order models mentioned above can be reduced to WFOMC (Van den Broeck et al 2011).…”

Section: Related Workmentioning

confidence: 99%

Lifted Inference with Tree Axioms

Bremen

Kuželka

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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We consider the problem of weighted first-order model counting (WFOMC): given a first-order sentence ϕ and domain size n ∈ ℕ, determine the weighted sum of models of ϕ over the domain {1, ..., n}. Past work has shown that any sentence using at most two logical variables admits an algorithm for WFOMC that runs in time polynomial in the given domain size (Van den Broeck 2011; Van den Broeck, Meert, and Darwiche 2014). In this paper, we extend this result to any two-variable sentence ϕ with the addition of a tree axiom, stating that some distinguished binary relation in ϕ forms a tree in the graph-theoretic sense.

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Section: Related Workmentioning

confidence: 99%

Lifted Inference with Tree Axioms

Bremen

Kuželka

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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“…Poole [23] introduces parametric factor graphs as relational models and proposes lifted variable elimination (LVE) as an exact inference algorithm on relational models. Other lifted inference algorithms include (i) the lifted junction tree algorithm (LJT) [6], (ii) first-order knowledge compilation [7], (iii) probabilistic theorem proving [11], and (iv) lifted belief propagation [1],…”

Section: Related Workmentioning

confidence: 99%

Restricting the Maximum Number of Actions for Decision Support Under Uncertainty

Gehrke

Braun

Polovina

2020

Ontologies and Concepts in Mind and Machine

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Standard approaches for decision support are computing a maximum expected utility or solving a partially observable Markov decision process. To the best of our knowledge, in both approaches, external restrictions are not accounted for. However, restrictions to actions often exists, for example in the form of limited resources. We demonstrate that restrictions to actions can lead to a combinatorial explosion if performed on a ground level, making ground inference intractable. Therefore, we extend a formalism that solves a lifted maximum expected utility problem to handle restricted actions. To test its relevance, we apply the new formalism to enterprise architecture analysis.

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“…Algorithm 1 outlines LJT for a set of queries (cf. (Braun and Möller 2016) for details). LJT starts with constructing an FO jtree.…”

Section: Parametric Factors (Parfactors) Combine Prvs As Argumentsmentioning

confidence: 99%

“…Taghipour et al formalise LVE by defining lifting operators while decoupling the constraint language from the operators (Taghipour et al 2013). The lifted junction tree algorithm (LJT) sets up a first-order junction tree (FO jtree) to handle multiple queries efficiently (Braun and Möller 2016), using LVE as a subroutine. LJT is based on the propositional junction tree algorithm (Lauritzen and Spiegelhalter 1988), which includes a junction tree (jtree) and a reasoning algorithm for efficient handling of multiple queries.…”

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confidence: 99%

Fusing First-Order Knowledge Compilation and the Lifted Junction Tree Algorithm

Braun

Möller

2018

Lecture Notes in Computer Science

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Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries as well as first-order knowledge compilation (FOKC) based on weighted model counting. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a model and LVE as a subroutine in its computations. For certain inputs, the implementations of LVE and, as a result, LJT ground parts of a model where FOKC has a lifted run. The purpose of this paper is to prepare LJT as a backbone for lifted inference and to use any exact inference algorithm as subroutine. Using FOKC in LJT allows us to compute answers faster than LJT, LVE, and FOKC for certain inputs. * PreliminariesThis section introduces notations and recap LJT. We specify a version of the smokers example (e.g., (van den Broeck et

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Lifted Junction Tree Algorithm

Cited by 32 publications

References 6 publications

Lifted Inference with Tree Axioms

Lifted Inference with Tree Axioms

Restricting the Maximum Number of Actions for Decision Support Under Uncertainty

Fusing First-Order Knowledge Compilation and the Lifted Junction Tree Algorithm

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