Department of Systems Engineering and Operations Research, George Mason University, 4400 University Dr, Fairfax, VA, USA, e-mails: mlocher@masonlive.gmu.edu, klaskey@gmu.edu, pcosta@gmu.edu"/>
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2020 Volume 35
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RESEARCH ARTICLE   Open Access    

Design patterns for modeling first-order expressive Bayesian networks

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  • Abstract: First-order expressive capabilities allow Bayesian networks (BNs) to model problem domains where the number of entities, their attributes, and their relationships can vary significantly between model instantiations. First-order BNs are well-suited for capturing knowledge representation dependencies, but literature on design patterns specific to first-order BNs is few and scattered. To identify useful patterns, we investigated the range of dependency models between combinations of random variables (RVs) that represent unary attributes, functional relationships, and binary predicate relationships. We found eight major patterns, grouped into three categories, that cover a significant number of first-order BN situations. Selection behavior occurs in six patterns, where a relationship/attribute identifies which entities in a second relationship/attribute are applicable. In other cases, certain kinds of embedded dependencies based on semantic meaning are exploited. A significant contribution of our patterns is that they describe various behaviors used to establish the RV’s local probability distribution. Taken together, the patterns form a modeling framework that provides significant insight into first-order expressive BNs and can reduce efforts in developing such models. To the best of our knowledge, there are no comprehensive published accounts of such patterns.
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  • Cite this article

    Mark Locher, Kathryn B. Laskey, Paulo C. G. Costa. 2020. Design patterns for modeling first-order expressive Bayesian networks. The Knowledge Engineering Review 35(1), doi: 10.1017/S026988892000034X
    Mark Locher, Kathryn B. Laskey, Paulo C. G. Costa. 2020. Design patterns for modeling first-order expressive Bayesian networks. The Knowledge Engineering Review 35(1), doi: 10.1017/S026988892000034X
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RESEARCH ARTICLE   Open Access    

Design patterns for modeling first-order expressive Bayesian networks

  • Received: 06 October 2018
  • Revised: 08 May 2020
  • Accepted: 14 May 2020
  • Published online: 17 June 2020
The Knowledge Engineering Review  35,  2020, 35(1)  |  Cite this article

Abstract: Abstract: First-order expressive capabilities allow Bayesian networks (BNs) to model problem domains where the number of entities, their attributes, and their relationships can vary significantly between model instantiations. First-order BNs are well-suited for capturing knowledge representation dependencies, but literature on design patterns specific to first-order BNs is few and scattered. To identify useful patterns, we investigated the range of dependency models between combinations of random variables (RVs) that represent unary attributes, functional relationships, and binary predicate relationships. We found eight major patterns, grouped into three categories, that cover a significant number of first-order BN situations. Selection behavior occurs in six patterns, where a relationship/attribute identifies which entities in a second relationship/attribute are applicable. In other cases, certain kinds of embedded dependencies based on semantic meaning are exploited. A significant contribution of our patterns is that they describe various behaviors used to establish the RV’s local probability distribution. Taken together, the patterns form a modeling framework that provides significant insight into first-order expressive BNs and can reduce efforts in developing such models. To the best of our knowledge, there are no comprehensive published accounts of such patterns.

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    Acknowledgments

    • The authors wish to thank the anonymous reviewer who provided insightful comments that allowed us to improve the paper.

    • The Xis may have direct dependencies (e.g. Xi may directly influence Xj, i≠j). These do not affect how the child RV LPD is developed.

    • It can enforce as many constraints as applicable to the same set of parents.

    • If they are the same RV, they must have different OVs, with constraints added that they cannot be the same entity.

    • SVs representing F-type states are ignored in the construction algorithm.

    • A template may have context variables that limit the entities that are present in a network. In general, the analysis here assumes no such context variables are in the template, unless there are two OVs from the same class and the model structure does not distinguish them.

    • Figure 5A has an unmodeled requirement that a room can have only one machine in it. It was not modeled because it adds additional nodes that clutter the point of the model and does not affect the LPD of MachineStatus. It could be modeled by including the remaining three MachineLocation nodes (for machines M2, M3, and M4) and adding a constraint node enforcing the requirement that each machine must be in a separate room. In Figure 5B, the constraint that a machine can be in only one room is modeled, using an embedded constraint approach. Note the state NA with 0 probability in RV MachineStatus_M1.

    • There is no claim that the dependency modeling approach establishes this dependency. Rather, the modeler identifies that this specific dependency exists in the domain being modeled.

    • |x| is cardinality of the class from which x is drawn.

    • They explored six different aggregator models, which used different mixes of data in the knowledge base. We selected one for this demonstration.

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    • © The Author(s), 2020. Published by Cambridge University Press2020Cambridge University Press
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    Mark Locher, Kathryn B. Laskey, Paulo C. G. Costa. 2020. Design patterns for modeling first-order expressive Bayesian networks. The Knowledge Engineering Review 35(1), doi: 10.1017/S026988892000034X
    Mark Locher, Kathryn B. Laskey, Paulo C. G. Costa. 2020. Design patterns for modeling first-order expressive Bayesian networks. The Knowledge Engineering Review 35(1), doi: 10.1017/S026988892000034X
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