The EM algorithm for graphical association models with missing data
Computational Statistics & Data Analysis - Special issue dedicated to Toma´sˇ Havra´nek
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Concrete Math
Gradient Descent Training of Bayesian Networks
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Exploiting causal independence in Bayesian network inference
Journal of Artificial Intelligence Research
Query DAGs: a practical paradigm for implementing belief-network inference
Journal of Artificial Intelligence Research
Local learning in probabilistic networks with hidden variables
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Goal oriented symbolic propagation in Bayesian networks
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Sensitivity analysis in discrete Bayesian networks
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
From Reliability Block Diagrams to Fault Tree Circuits
Decision Analysis
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We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial derivatives of this polynomial with respect to each variable. We show that once such derivatives are made available, one can compute in constant-time answers to a large class of probabilistic queries, which are central to classical inference, parameter estimation, model validation and sensitivity analysis. We present a number of complexity results relating to the compilation of such polynomials and to the computation of their partial derivatives. We argue that the combined simplicity, comprehensiveness and computational complexity of the presented framework is unique among existing frameworks for inference in Bayesian networks.