Hierarchical Data Structures and Algorithms for Computer Graphics. Part I.
IEEE Computer Graphics and Applications
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Elements of information theory
Elements of information theory
Causal Probabilistic Networks with Both Discrete and Continuous Variables
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implementation of continuous Bayesian networks using sums of weighted Gaussians
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Evolution of Multi-adaptive Discretization Intervals for a Rule-Based Genetic Learning System
IBERAMIA 2002 Proceedings of the 8th Ibero-American Conference on AI: Advances in Artificial Intelligence
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
Computing Intervals of Probabilities with Simulated Annealing and Probability Trees
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
CCIA '02 Proceedings of the 5th Catalonian Conference on AI: Topics in Artificial Intelligence
Predicting software defects in varying development lifecycles using Bayesian nets
Information and Software Technology
Approximate probability propagation with mixtures of truncated exponentials
International Journal of Approximate Reasoning
Inference in hybrid Bayesian networks using dynamic discretization
Statistics and Computing
Wrapper discretization by means of estimation of distribution algorithms
Intelligent Data Analysis
Efficient belief propagation for higher-order cliques using linear constraint nodes
Computer Vision and Image Understanding
Arc reversals in hybrid Bayesian networks with deterministic variables
International Journal of Approximate Reasoning
Binary Probability Trees for Bayesian Networks Inference
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Maximum Likelihood Learning of Conditional MTE Distributions
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Generalized evidence pre-propagated importance sampling for hybrid Bayesian networks
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
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
Comparing risks of alternative medical diagnosis using Bayesian arguments
Journal of Biomedical Informatics
Environmental Modelling & Software
Approximate inference in Bayesian networks using binary probability trees
International Journal of Approximate Reasoning
Recursive probability trees for Bayesian networks
CAEPIA'09 Proceedings of the Current topics in artificial intelligence, and 13th conference on Spanish association for artificial intelligence
Review: Bayesian networks in environmental modelling
Environmental Modelling & Software
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
Interpolating conditional density trees
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Exact inference in networks with discrete children of continuous parents
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
MICAI'06 Proceedings of the 5th Mexican international conference on Artificial Intelligence
Mixtures of truncated basis functions
International Journal of Approximate Reasoning
Penniless propagation with mixtures of truncated exponentials
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Modeling conditional distributions of continuous variables in bayesian networks
IDA'05 Proceedings of the 6th international conference on Advances in Intelligent Data Analysis
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
Availability modelling of repairable systems using Bayesian networks
Engineering Applications of Artificial Intelligence
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
Discretization methods for NBC in effort estimation: an empirical comparison based on ISBSG projects
Proceedings of the ACM-IEEE international symposium on Empirical software engineering and measurement
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a nonuniform partition across all variables as opposed to uniform partition of each variable separately reduces the size of the data structures needed to represent a continuous function. We also provide a simple but efficient procedure for nonuniform partition. To represent a nonuniform discretization in the computer memory, we introduce a new data structure, which we call a Binary Split Partition (BSP) tree. We show that BSP trees can be an exponential factor smaller than the data structures in the standard uniform discretization in multiple dimensions and show how the BSP trees can be used in the standard join tree algorithm. We show that the accuracy of the inference process can be significantly improved by adjusting discretization with evidence. We construct an erative anytime algorithm that gradually improves the quality of the discretization and the accuracy of the answer on a query. We provide empirical evidence that the algorithm converges.