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Generalized Weighted Model Counting: An Efficient Monte-Carlo meta-algorithm (Working Paper)

  • Lirong Xia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

In this paper, we focus on computing the prices of securities represented by logical formulas in combinatorial prediction markets when the price function is represented by a Bayesian network. This problem turns out to be a natural extension of the weighted model counting (WMC) problem [1], which we call generalized weighted model counting (GWMC) problem. In GWMC, we are given a logical formula F and a polynomial-time computable weight function. We are asked to compute the total weight of the valuations that satisfy F.

Based on importance sampling, we propose a Monte-Carlo meta-algorithm that has a good theoretical guarantee for formulas in disjunctive normal form (DNF). The meta-algorithm queries an oracle algorithm that computes marginal probabilities in Bayesian networks, and has the following theoretical guarantee. When the weight function can be approximately represented by a Bayesian network for which the oracle algorithm runs in polynomial time, our meta-algorithm becomes a fully polynomial-time randomized approximation scheme (FPRAS).

References

  1. 1.
    Sang, T., Bearne, P., Kautz, H.: Performing bayesian inference by weighted model counting. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Pittsburgh, PA, USA, pp. 475–481 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lirong Xia
    • 1
  1. 1.SEASHarvard UniversityUSA

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