Nonlinear deterministic relationships in bayesian networks

Authors:
Barry R. Cobb;Prakash P. Shenoy
Affiliations:
University of Kansas School of Business, Lawrence, KS;University of Kansas School of Business, Lawrence, KS
Venue:
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2005

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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.