Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Operations Research
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
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
Inference in hybrid Bayesian networks with mixtures of truncated exponentials
International Journal of Approximate Reasoning
Parameter estimation and model selection for mixtures of truncated exponentials
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
From influence diagrams to junction trees
UAI'94 Proceedings of the Tenth international 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
International Journal of Approximate Reasoning
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
Review: Bayesian networks in environmental modelling
Environmental Modelling & Software
Mixtures of truncated basis functions
International Journal of Approximate Reasoning
Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks
International Journal of Approximate Reasoning
Answering queries in hybrid Bayesian networks using importance sampling
Decision Support Systems
Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Learning mixtures of truncated basis functions from data
International Journal of Approximate Reasoning
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The main goal of this paper is to describe inference in hybrid Bayesian networks (BNs) using mixture of polynomials (MOP) approximations of probability density functions (PDFs). Hybrid BNs contain a mix of discrete, continuous, and conditionally deterministic random variables. The conditionals for continuous variables are typically described by conditional PDFs. A major hurdle in making inference in hybrid BNs is marginalization of continuous variables, which involves integrating combinations of conditional PDFs. In this paper, we suggest the use of MOP approximations of PDFs, which are similar in spirit to using mixtures of truncated exponentials (MTEs) approximations. MOP functions can be easily integrated, and are closed under combination and marginalization. This enables us to propagate MOP potentials in the extended Shenoy-Shafer architecture for inference in hybrid BNs that can include deterministic variables. MOP approximations have several advantages over MTE approximations of PDFs. They are easier to find, even for multi-dimensional conditional PDFs, and are applicable for a larger class of deterministic functions in hybrid BNs.