Focused most probable world computations in probabilistic logic programs

  • Gerardo I. Simari
  • Maria Vanina Martinez
  • Amy Sliva
  • V. S. Subrahmanian
Article

DOI: 10.1007/s10472-012-9285-y

Cite this article as:
Simari, G.I., Martinez, M.V., Sliva, A. et al. Ann Math Artif Intell (2012) 64: 113. doi:10.1007/s10472-012-9285-y
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Abstract

The “Most Probable World” (MPW) problem in probabilistic logic programming (PLPs) is that of finding a possible world with the highest probability. Past work has shown that this problem is computationally intractable and involves solving exponentially many linear programs, each of which is of exponential size. In this paper, we study what happens when the user focuses his interest on a set of atoms in such a PLP. We show that we can significantly reduce the number of worlds to be considered by defining a “reduced” linear program whose solution is in one-one correspondence with the exact solution to the MPW problem. However, the problem is still intractable. We develop a Monte Carlo sampling approach that enables us to build a quick approximation of the reduced linear program that allows us to estimate (inexactly) the solution to the MPW problem. We show experimentally that our approach works well in practice, scaling well to problems where the exact solution is intractable to compute.

Keywords

Probabilistic logic programming Imprecise probabilities Most probable worlds 

Mathematics Subject Classifications (2010)

68T37 68T30 68T27 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Gerardo I. Simari
    • 1
    • 2
  • Maria Vanina Martinez
    • 1
    • 2
  • Amy Sliva
    • 1
    • 2
  • V. S. Subrahmanian
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of Maryland College ParkCollege ParkUSA
  2. 2.University of Maryland Institute for Advanced Computer Studies (UMIACS)University of Maryland College ParkCollege ParkUSA

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