Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 2, 265--288

Some Structural Approximations for Efficient Probability Propagation in Evolving High Dimensional Gaussian Processes

A.S. Gargoum, UAE University, Al Ain, United Arab Emirates

SUMMARY. One of the main issues that have emerged from learning Bayesian networks from data is the need for computational efficiency. In recent years, it has been shown that exact probabilistic propagation algorithms can be used for a quick and efficient absorption of information on dynamic junction trees of cliques. These algorithms were applied on Gaussian networks, where the underlying relationships between variables evolve dynamically. However, these algorithms work when each observation is taken under only a single clique of the original junction tree. In this paper, I outline how approximate techniques can be used to address the issue of how to adapt the system when an observation is taken under several cliques and consequently improve the system speed. These approximations are used in conjunction with Kullback-Leibler divergence or Hellinger distance between the true density and its approximation to indicate the approximation accuracy.

AMS (2000) subject classification. Primary 62F15.

Key words and phrases. Bayesian networks, graphical modeling, junction trees, probability propagation.

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