Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials |
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Authors: | Barry R Cobb Prakash P Shenoy Rafael Rumí |
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Institution: | 1. Department of Economics and Business, Virginia Military Institute, Lexington, VA, 24450 2. University of Kansas School of Business, 1300 Sunnyside Ave., Summerfield Hall, Lawrence, KS, 66045–7585 3. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Ctra. Sacramento s/n, La Ca?ada de San Urbano, 04120, Almería, Spain
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Abstract: | Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving
hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always
be marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer architecture for computing
marginals, with no restrictions on the construction of a join tree. This paper presents MTE potentials that approximate standard
PDF’s and applications of these potentials for solving inference problems in hybrid Bayesian networks. These approximations
will extend the types of inference problems that can be modelled with Bayesian networks, as demonstrated using three examples. |
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Keywords: | Graphs and networks Probabilistic computation Modeling methodologies Bayesian networks |
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