Scalable Parallel Implementation of Bayesian Network to Junction Tree Conversion for Exact Inference

We present a scalable parallel implementation for converting a Bayesian network to a junction tree, which can then be used for a complete parallel implementation for exact inference. We explore parallelism during the process of moralization, triangulation, clique identification, junction tree construction and potential table calculation. For an arbitrary Bayesian network with n vertices using p processors, the worst-case running time is shown to be O(n2w/p+-wrwn/p+n log p), where w is the clique width and r is the number of states of the random variables. Our algorithm is scalable over 1 les p les nw/log n. We have implemented our parallel algorithm using OpenMP and experimented with up to 128 processors. We consider three types of Bayesian networks: linear, balanced and random. While the state of the art PNL library implementation does not scale, we achieve speedups of 31, 29 and 24 for the above graphs respectively on the DataStar cluster at San Diego Supercomputing Center

[1]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[2]  Dan Geiger,et al.  A sufficiently fast algorithm for finding close to optimal junction trees , 1996, UAI.

[3]  Ross D. Shachter,et al.  Global Conditioning for Probabilistic Inference in Belief Networks , 1994, UAI.

[4]  David M. Pennock.  Logarithmic Time Parallel Bayesian Inference , 1998, UAI.

[5]  Zhaoyu Li,et al.  Parallelizing Probabilistic Inference: Some Early Explorations , 1992, UAI.

[6]  Jaswinder Pal Singh,et al.  A parallel Lauritzen-Spiegelhalter algorithm for probabilistic inference , 1994, Proceedings of Supercomputing '94.

[7]  Ben Taskar,et al.  Rich probabilistic models for gene expression , 2001, ISMB.

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

[9]  Jaswinder Pal Singh,et al.  Parallel Implementations of Probabilistic Inference , 1996, Computer.

[10]  José Mira,et al.  DISTRIBUTED INFERENCE IN BAYESIAN NETWORKS , 1994 .

[11]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[12]  Viktor K. Prasanna,et al.  Scalable parallel implementation of exact inference in Bayesian networks , 2006, 12th International Conference on Parallel and Distributed Systems - (ICPADS'06).

[13]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[14]  David Heckerman,et al.  Bayesian Networks for Data Mining , 2004, Data Mining and Knowledge Discovery.