## Approximating Bayesian Belief Networks by Arc Removal (1997)

Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 21 - 0 self |

### BibTeX

@ARTICLE{Engelen97approximatingbayesian,

author = {Robert A. Van Engelen},

title = {Approximating Bayesian Belief Networks by Arc Removal},

journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

year = {1997},

volume = {19},

pages = {916--920}

}

### Years of Citing Articles

### OpenURL

### Abstract

Bayesian belief networks or causal probabilistic networks may reach a certain size and complexity where the computations involved in exact probabilistic inference on the network tend to become rather time consuming. Methods for approximating a network by a simpler one allow the computational complexity of probabilistic inference on the network to be reduced at least to some extend. We propose a general framework for approximating Bayesian belief networks based on model simplification by arc removal. The approximation method aims at reducing the computational complexity of probabilistic inference on a network at the cost of introducing a bounded error in the prior and posterior probabilities inferred. We present a practical approximation scheme and give some preliminary results. 1 Introduction Today, more and more applications based on the Bayesian belief network 1 formalism are emerging for reasoning and decision making in problem domains with inherent uncertainty. Current applicati...

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Citation Context ...i j c G (V i ) ) = 1 \Gamma fl V i (v i j c G (V i ) ), i = 1; : : : ; n. A probabilistic meaning is assigned to the topology of the digraph of a belief network by means of the d-separation criterion =-=[18]-=-. The criterion allows for the detection of dependency relationships between the vertices of the network's digraph by traversing undirected paths, called chains, comprised by the directed links in the... |

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Citation Context ...been mentioned above, Kjaerulff's method operates only with the Bayesian belief universe approach to probabilistic inference using the clique-tree propagation algorithm of Lauritzen and Spiegelhalter =-=[16]-=-. In contrast, the framework we propose operates on a network directly and therefore applies to any type of method for probabilistic inference. Finally, given an upper bound on the posterior error in ... |

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Citation Context ...ference increases dramatically, reaching a state where real-time decision making eventually becomes prohibitive; exact inference in general with Bayesian belief networks has been proven to be NP-hard =-=[3]-=-. For many applications, computing exact probabilities from a belief network is liable to be unrealistic due to inaccuracies in the probabilistic assessments for the network. Therefore, in general, ap... |

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Citation Context ... general, the KullbackLeibler information divergence statistic [14] provides a means for measuring the divergence between a probability distribution and an approximation of the distribution, see e.g. =-=[22]-=-. However, there are important differences to be noted between the approaches. Firstly, the type of independence statements enforced in our approach renders the direct dependence relationship portraye... |

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Citation Context ...irection towards belief network approximation in view of model simplification. However, Kjaerulff's method is specifically tailored to the Bayesian belief universe approach to probabilistic inference =-=[9]-=- and model simplification is not applied to a network directly but to the belief universes obtained from a belief network. The method identifies weak dependencies in a belief universe of a network and... |

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Citation Context ...tic networks, causal networks, and recursive models. 1 if the generated multiset is sufficiently large. Unfortunately, the computational complexity of approximate methods is still known to be NP-hard =-=[5]-=- if a certain accuracy of the probability estimates is demanded for. Hence, just like exact methods, simulation methods have an exponential worst-case computational complexity. As has been demonstrate... |

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Citation Context ...onstraintsd(Pr; A)s" psensures that the error in the prior and posterior probability distribution never exceeds ". This optimization problem can be solved by employing a simulated annealing =-=technique [12]-=-, or by using an evolutionary algorithm [17], to find a linear set of arcs for removal that is nearly optimal. A `real' optimal solution is not appropriate to search for, since only heuristic function... |

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Citation Context ... algorithms have been developed from which Pearl's polytree algorithm with cutset conditioning [18, 19] and the method of clique-tree propagation by Lauritzen and Spiegelhalter [16] (and combinations =-=[20]-=-) are the most widely used algorithms for exact probabilistic inference. Simulation methods provide for approximate probabilistic inference, see [4] for an overview. 2.2 Information Theory The Kullbac... |

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