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Probabilistic reasoning in intelligent systems: networks of plausible inference
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A compiler for deterministic, decomposable negation normal form
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Exploiting causal independence in Bayesian network inference
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When do numbers really matter?
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Local learning in probabilistic networks with hidden variables
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Goal oriented symbolic propagation in Bayesian networks
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MAP complexity results and approximation methods
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Bucket elimination: a unifying framework for probabilistic inference
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On-line alert systems for production plants: A conflict based approach
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Case-factor diagrams for structured probabilistic modeling
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Logical Compilation of Bayesian Networks with Discrete Variables
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Diagnosing faults in electrical power systems of spacecraft and aircraft
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Complexity results and approximation strategies for MAP explanations
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International Journal of Approximate Reasoning
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We present a new approach to inference in Bayesian networks, which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it can be computed efficiently using an arithmetic circuit that can be evaluated and differentiated in time and space linear in the circuit size. The proposed framework for inference subsumes one of the most influential methods for inference in Bayesian networks, known as the tree-clustering or jointree method, which provides a deeper understanding of this classical method and lifts its desirable characteristics to a much more general setting. We discuss some theoretical and practical implications of this subsumption.