Annual review of computer science: vol. 3, 1988
A Differential Approach to Inference in Bayesian Networks
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
When do Numbers Really Matter?
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
Local learning in probabilistic networks with hidden variables
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
SPUDD: stochastic planning using decision diagrams
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
On probabilistic inference by weighted model counting
Artificial Intelligence
Compiling Bayesian networks using variable elimination
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Compiling relational Bayesian networks for exact inference
International Journal of Approximate Reasoning
Understanding the scalability of Bayesian network inference using clique tree growth curves
Artificial Intelligence
Probabilistic model-based diagnosis: an electrical power system case study
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
The inclusion-exclusion rule and its application to the junction tree algorithm
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions. According to this approach, belief network inference reduces to a simple process of evaluating and differentiating multilinear functions. We show here that mainstream inference algorithms based on jointrees are a special case of the approach based on multi-linear functions, in a very precise sense. We use this result to prove new properties of jointree algorithms. We also discuss some practical and theoretical implications of this new finding.