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).
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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)
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© 2012 Springer-Verlag Berlin Heidelberg
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Xia, L. (2012). Generalized Weighted Model Counting: An Efficient Monte-Carlo meta-algorithm (Working Paper). In: Goldberg, P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35311-6_48
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DOI: https://doi.org/10.1007/978-3-642-35311-6_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35310-9
Online ISBN: 978-3-642-35311-6
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