Pre-processing for triangulation of probabilistic networks

Authors:
Hans L. Bodlaender;Arie M. C. A. Koster;Frank van den Eijkhof;Linda C. van der Gaag
Affiliations:
Institute of Information and Computing, Sciences, Utrecht University, The Netherlands;Konrad-Zuse-Zentrum, für Informationstechnik Berlin, Berlin-Dahlem, Germany;Institute of Information and Computing Sciences, Utrecht University, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, The Netherlands
Venue:
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Year:
2001

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Abstract

The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph. The reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by pre-processing; for other networks, huge reductions in size are obtained.