Mixtures of Truncated Exponentials in Hybrid Bayesian Networks
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Inference in hybrid Bayesian networks using mixtures of polynomials
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks
International Journal of Approximate Reasoning
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We discuss some issues in using mixtures of polynomials (MOPs) for inference in hybrid Bayesian networks. MOPs were proposed by Shenoy and West for mitigating the problem of integration in inference in hybrid Bayesian networks. In definingMOP for multi-dimensional functions, one requirement is that the pieces where the polynomials are defined are hypercubes. In this paper, we discuss relaxing this condition so that each piece is defined on regions called hyper-rhombuses. This relaxation means that MOPs are closed under transformations required for multi-dimensional linear deterministic conditionals, such as Z = X + Y. Also, this relaxation allows us to construct MOP approximations of the probability density functions (PDFs) of the multi-dimensional conditional linear Gaussian distributions using a MOP approximation of the PDF of the univariate standard normal distribution. We illustrate our method using conditional linear Gaussian PDFs in two and three dimensions.