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Nonlinear Deterministic Relationships in Bayesian Networks
Cobb, Barry R. Shenoy, Prakash P.
Cobb, Barry R.
Shenoy, Prakash P.
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Abstract
In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations required for performing inference with nonlinear conditionally deterministic variables are developed. We perform inference in networks with nonlinear deterministic variables and non-Gaussian continuous variables by using piecewise linear approximations to nonlinear functions and modeling probability distributions with mixtures of truncated exponentials (MTE) potentials.
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Date
2005-07
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Springer-Verlag
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Keywords
Conditionally deterministic variables, Mixtures of truncated exponentials, Conditional linear gaussian distributions
Citation
Cobb, B. R. and P. P. Shenoy (2005), "Nonlinear Deterministic Relationships in Bayesian Networks," in L. Godo (ed.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Lecture Notes in Artificial Intelligence 3571, 27--38, Springer-Verlag, Berlin.