Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Operations Research
Probabilistic inference and influence diagrams
Operations Research
Management Science
Valuation-based systems for Bayesian decision analysis
Operations Research
Distributions in the physical and engineering sciences
Distributions in the physical and engineering sciences
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
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
On-line alert systems for production plants: A conflict based approach
International Journal of Approximate Reasoning
Belief update in CLG Bayesian networks with lazy propagation
International Journal of Approximate Reasoning
Arc reversals in hybrid Bayesian networks with deterministic variables
International Journal of Approximate Reasoning
Inference in Hybrid Bayesian Networks with Deterministic Variables
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Learning hybrid Bayesian networks using mixtures of truncated exponentials
International Journal of Approximate Reasoning
Parameter estimation and model selection for mixtures of truncated exponentials
International Journal of Approximate Reasoning
Inference in hybrid Bayesian networks using mixtures of polynomials
International Journal of Approximate Reasoning
A variational approximation for Bayesian networks with discrete and continuous latent variables
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Inference in hybrid networks: theoretical limits and practical algorithms
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Nonlinear deterministic relationships in bayesian networks
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A re-definition of mixtures of polynomials for inference in hybrid Bayesian networks
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks
International Journal of Approximate Reasoning
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The main goal of this paper is to describe an architecture for solving large general hybrid Bayesian networks (BNs) with deterministic conditionals for continuous variables using local computation. In the presence of deterministic conditionals for continuous variables, we have to deal with the non-existence of the joint density function for the continuous variables. We represent deterministic conditional distributions for continuous variables using Dirac delta functions. Using the properties of Dirac delta functions, we can deal with a large class of deterministic functions. The architecture we develop is an extension of the Shenoy-Shafer architecture for discrete BNs. We extend the definitions of potentials to include conditional probability density functions and deterministic conditionals for continuous variables. We keep track of the units of continuous potentials. Inference in hybrid BNs is then done in the same way as in discrete BNs but by using discrete and continuous potentials and the extended definitions of combination and marginalization. We describe several small examples to illustrate our architecture. In addition, we solve exactly an extended version of the crop problem that includes non-conditional linear Gaussian distributions and non-linear deterministic functions.