Abstract
We show that a number of problems in Artificial Intelligence can be seen as Stochastic Constraint Optimization Problems (SCOPs): problems that have both a stochastic and a constraint optimization component. We argue that these problems can be modeled in a new language, SC-ProbLog, that combines a generic Probabilistic Logic Programming (PLP) language, ProbLog, with stochastic constraint optimization. We propose a toolchain for effectively solving these SC-ProbLog programs, which consists of two stages. In the first stage, decision diagrams are compiled for the underlying distributions. These diagrams are converted into models that are solved using Mixed Integer Programming or Constraint Programming solvers in the second stage. We show that, to yield linear constraints, decision diagrams need to be compiled in a specific form. We introduce a new method for compiling small Sentential Decision Diagrams in this form. We evaluate the effectiveness of several variations of this toolchain on test cases in viral marketing and bioinformatics.
A.L.D. Latour wishes to thank KU Leuven, since the inspiration for this work came during a research visit to its Computer Science Department. She also wishes to thank Université catholique de Louvain, since the work itself was done during a research visit to its ICTEAM institute.
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Notes
- 1.
See http://probabilistic-programming.org/ for a recent list of systems.
- 2.
- 3.
Using the big M-approach [19] with \(M\le 1\), as all real values are probabilities.
- 4.
Available at https://gephi.org/.
- 5.
Available at www.gurobi.com and www.gecode.org.
- 6.
Availabe at https://dtai.cs.kuleuven.be/problog/.
- 7.
Available at http://reasoning.cs.ucla.edu/sdd/.
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Acknowledgements
We thank Luc De Raedt for his support, for his advice and for the numerous other ways in which he contributed to this work. This research was supported by the Netherlands Organisation for Scientific Research (NWO) and NSF grant #IIS-1657613.
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Latour, A.L.D., Babaki, B., Dries, A., Kimmig, A., Van den Broeck, G., Nijssen, S. (2017). Combining Stochastic Constraint Optimization and Probabilistic Programming. 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_32
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