论文信息 - Evaluation of hybrid Bayesian networks using analytical density representations

Evaluation of hybrid Bayesian networks using analytical density representations

Abstract In this article, a new mechanism is described for modeling and evaluating Hybrid Dynamic Bayesian networks. The approach uses Gaussian mixtures and Dirac mixtures as messages to calculate marginal densities. As these densities are approximated by means of Gaussian mixtures, any desired precision is possible. The presented approach removes the restrictions of sample based evaluation of Bayesian networks since it uses an analytical approximation scheme for probability densities which systematically minimizes the distance between the exact and the approximate density.

O. C. Schrempf | U. Hanebeck

[1] N. Wermuth,et al. Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative , 1989 .

[2] Judea Pearl,et al. Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[3] S. Lauritzen. Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[4] Kristian G. Olesen,et al. Causal Probabilistic Networks with Both Discrete and Continuous Variables , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[5] Darryl Morrell,et al. Implementation of Continuous Bayesian Networks Using Sums of Weighted Gaussians , 1995, UAI.

[6] Kevin P. Murphy,et al. A Variational Approximation for Bayesian Networks with Discrete and Continuous Latent Variables , 1999, UAI.

[7] Uri Lerner,et al. Exact Inference in Networks with Discrete Children of Continuous Parents , 2001, UAI.

[8] Kevin Murphy,et al. Dynamic Bayesian Networks , 2002 .

[9] Uwe D. Hanebeck,et al. Progressive Bayes: a new framework for nonlinear state estimation , 2003, SPIE Defense + Commercial Sensing.

[10] Uwe D. Hanebeck,et al. A New Approach for Hybrid Bayesian Networks Using Full Densities , 2004 .