Mixtures of Truncated Exponentials in Hybrid Bayesian Networks

In this paper we propose the use of mixtures of truncated exponential (MTE) distributions in hybrid Bayesian networks. We study the properties of the MTE distribution and show how exact probability propagation can be carried out by means of a local computation algorithm. One feature of this model is that no restriction is made about the order among the variables either discrete or continuous. Computations are performed over a representation of probabilistic potentials based on probability trees, expanded to allow discrete and continuous variables simultaneously. Finally, a Markov chain Monte Carlo algorithm is described with the aim of dealing with complex networks.

[1]  Daphne Koller,et al.  Nonuniform Dynamic Discretization in Hybrid Networks , 1997, UAI.

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

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

[4]  Dragomir Anguelov,et al.  A General Algorithm for Approximate Inference and Its Application to Hybrid Bayes Nets , 1999, UAI.

[5]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[6]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[7]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[9]  Anders L. Madsen,et al.  LAZY Propagation: A Junction Tree Inference Algorithm Based on Lazy Evaluation , 1999, Artif. Intell..

[10]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[11]  Serafín Moral,et al.  Penniless propagation in join trees , 2000 .

[12]  A. Salmerón,et al.  Importance sampling in Bayesian networks using probability trees , 2000 .

[13]  Judea Pearl,et al.  Evidential Reasoning Using Stochastic Simulation of Causal Models , 1987, Artif. Intell..

[14]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .