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On Learning When to Decompose Graphical Models

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Learning and Intelligent Optimization (LION 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14286))

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Abstract

Decomposition is a well-known algorithmic technique for Graphical Models. It is commonly believed that such a technique is cost-effective for instances with low width. In this paper, we show on a large data set of real-life inspired instances that this is not the case. To better understand this result, we narrow our study and consider k-tree instances where the width is well controlled and get similar results. Finally, we show that by adding a few simple features and using simple Machine Learning models we can predict the convenience to decompose with an accuracy of more than \(85\%\), which produces time reductions in standard benchmarks of nearly \(90\%\).

Supported by grant PID2021-122830OB-C43, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF: A way of making Europe”.

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Notes

  1. 1.

    A line of work under the name of soft global constraints extends this definition by allowing large scope cost functions as long as the functions are tractable.

  2. 2.

    Note that this corresponds to solving the problem with dynamic programming implemented with memoization.

  3. 3.

    http://genoweb.toulouse.inra.fr/~degivry/evalgm/.

  4. 4.

    https://forgemia.inra.fr/thomas.schiex/cost-function-library.

  5. 5.

    https://toulbar2.github.io/toulbar2/index.html.

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Authors and Affiliations

  1. UPC Barcelona Tech, Barcelona, Spain

    Aleksandra Petrova & Javier Larrosa

Authors
  1. Aleksandra Petrova
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  2. Javier Larrosa
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Correspondence to Aleksandra Petrova .

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Editors and Affiliations

  1. InsideOpt, Dover, DE, USA

    Meinolf Sellmann

  2. Bielefeld University, Bielefeld, Germany

    Kevin Tierney

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Petrova, A., Larrosa, J. (2023). On Learning When to Decompose Graphical Models. In: Sellmann, M., Tierney, K. (eds) Learning and Intelligent Optimization. LION 2023. Lecture Notes in Computer Science, vol 14286. Springer, Cham. https://doi.org/10.1007/978-3-031-44505-7_19

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  • DOI: https://doi.org/10.1007/978-3-031-44505-7_19

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