Tracking and data association
Simulation Approaches to General Probabilistic Inference on Belief Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Variational Approximations between Mean Field Theory and the Junction Tree Algorithm
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Bayesian Fault Detection and Diagnosis in Dynamic Systems
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
A general algorithm for approximate inference and its application to hybrid bayes nets
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
A variational approximation for Bayesian networks with discrete and continuous latent variables
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Nonuniform dynamic discretization in hybrid networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part II
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
Multilevel Bayesian networks for the analysis of hierarchical health care data
Artificial Intelligence in Medicine
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Many real life domains contain a mixture of discrete and continuous variables and can be modeled as hybrid Bayesian Networks (BNs). An important subclass of hybrid BNs are conditional linear Gaussian (CLG) networks, where the conditional distribution of the continuous variables given an assignment to the discrete variables is a multivariate Gaussian. Lauritzen's extension to the clique tree algorithm can be used for exact inference in CLG networks. However, many domains include discrete variables that depend on continuous ones, and CLG networks do not allow such dependencies to be represented. In this paper, we propose the first "exact" inference algorithm for augmented CLG networks -- CLG networks augmented by allowing discrete children of continuous parents. Our algorithm is based on Lauritzen's algorithm, and is exact in a similar sense: it computes the exact distributions over the discrete nodes, and the exact first and second moments of the continuous ones, up to inaccuracies resulting from numerical integration used within the algorithm. In the special case of softmax CPDs, we show that integration can often be done efficiently, and that using the first two moments leads to a particularly accurate approximation. We show empirically that our algorithm achieves substantially higher accuracy at lower cost than previous algorithms for this task.