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MDDs: Sampling and Probability Constraints

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Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

We propose to combine two successful techniques of Artificial Intelligence: sampling and Multi-valued Decision Diagrams (MDDs). Sampling, and notably Markov sampling, is often used to generate data resembling to a corpus. However, this generation has usually to respect some additional constraints, for instance to avoid plagiarism or to respect some rules of the application domain. We propose to represent the corpus dependencies and these side constraints by an MDD and to develop some algorithms for sampling the solutions of an MDD while respecting some probabilities or a Markov chain. In that way, we obtain a generic method which avoids the development of ad-hoc algorithms for each application as it is currently the case. In addition, we introduce new constraints for controlling the probabilities of the solutions that are sampled. We experiments our method on a real life application: the geomodeling of a petroleum reservoir, and on the generation of French alexandrines. The obtained results show the advantage and the efficiency of our approach.

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Notes

  1. 1.

    Order k Markov chains have a longer memory: the Markov property states that \(P(X_i |X_1, \ldots , X_{i-1}) = P(X_i |X_{i-k}, \ldots , X_{i-1})\). They are equivalent to order 1 Markov chains on an alphabet composed of k-grams, and therefore we assume only order 1 Markov chains [17].

  2. 2.

    vv(n) represents a vector of v(n).

  3. 3.

    We can also directly deal with products if we modify the costMDD propagator accordingly.

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Acknowledgements

This research is conducted within the Flow Machines project which received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement no. 291156. We would like to thank F. Pachet and P. Roy, who gave us the idea of this article.

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Authors and Affiliations

  1. Université Nice-Sophia Antipolis, I3S UMR 7271, CNRS, Sophia Antipolis, France

    Guillaume Perez & Jean-Charles Régin

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  1. Guillaume Perez
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  2. Jean-Charles Régin
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Correspondence to Jean-Charles Régin .

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Editors and Affiliations

  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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Perez, G., Régin, JC. (2017). MDDs: Sampling and Probability Constraints. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_15

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