## AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks (2000)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 72 - 4 self |

### BibTeX

@ARTICLE{Cheng00ais-bn:an,

author = {Jian Cheng and Marek J. Druzdzel},

title = {AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks},

journal = {Journal of Artificial Intelligence Research},

year = {2000},

volume = {13},

pages = {13--155}

}

### Years of Citing Articles

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### Abstract

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in nite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from dierent stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, lik...

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Citation Context ...unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by thesrst few iterations of the AIS-BN algorithm. 1. Introduction Bayesian networks (=-=Pearl, 1988-=-) are increasingly popular tools for modeling uncertainty in intelligent systems. With practical models reaching the size of several hundreds of variables (e.g., Pradhan et al., 1994; Conati et al., 1... |

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Citation Context ...bility of probabilistic inference. Even though several ingenious exact algorithms have been proposed, in very large models they all stumble on the theoretically demonstrated NP-hardness of inference (=-=Cooper, 199-=-0). The signicance of this result can be observed in practice | exact algorithms applied to large, densely connected practical networks require either a prohibitive amount of memory or a prohibitive a... |

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Citation Context ...(Section 2.1), any technique that can reduce the variance 2 Pr(e) will reduce the variance of c Pr(e) and correspondingly improve the sampling performance. Since the variance of stratied sampling (Ru=-=binstein, 1981-=-) is never much worse than that of random sampling, and can be much better, it can improve the convergence rate. We expect some other variance reduction methods in statistics, such as: (i) the expecte... |

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Citation Context ...(aje) obtained by means of Equation 7 is not an unbiased estimator. However, as the number of samples increases, the bias decreases and can be ignored altogether when the sample size is large enough (=-=Fishman, 1995-=-). Figure 1 presents a generic stochastic sampling algorithm that captures most of the existing sampling algorithms. Without the loss of generality, we restrict ourselves in our description to so-call... |

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Citation Context ...ng, will also improve the sampling performance. Current learning algorithm used a simple approach. Some heuristic learning methods, such as adjusting learning rates according to changes of the error (=-=Jacobs, 1988-=-), should also be applicable to our algorithm. There are several tunable parameters in the AIS-BN algorithm. Finding the optimal values of these parameters for any given network is another interesting... |

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Citation Context ...lled Markov Chain Monte Carlo (MCMC) methods that are divided into Gibbs sampling, Metropolis sampling, and Hybrid Monte Carlo sampling (Geman & Geman, 1984; Gilks, Richardson, & Spiegelhalter, 1996; =-=MacKay, 1998-=-). Roughly speaking, these methods draw random samples from an unknown target distribution f(X) by biasing the search for this distribution towards higher probability regions. When applied to Bayesian... |

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Citation Context ...ombinations of the parent nodes. It is possible that conditional probability distributions with causal independence properties, such as Noisy-OR distributions (Pearl, 1988; Henrion, 1989; Diez, 1993; =-=Srinivas, 199-=-3; Heckerman & Breese, 1994), common in very large practical networks, can be treated dierently and lead to considerable savings in the learning time. One direction of testing approximate algorithms, ... |

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Citation Context ... under all combinations of the parent nodes. It is possible that conditional probability distributions with causal independence properties, such as Noisy-OR distributions (Pearl, 1988; Henrion, 1989; =-=Diez, 199-=-3; Srinivas, 1993; Heckerman & Breese, 1994), common in very large practical networks, can be treated dierently and lead to considerable savings in the learning time. One direction of testing approxim... |

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Citation Context ...al. (1991) (k) = a b a k=kmax ; (10) where a is the initial learning rate and b is the learning rate in the last step. This function has been reported to perform well in neural network learning (Rit=-=ter et al., 1991-=-). 3.3 Heuristic Initialization in AIS-BN The dimensionality of the problem of Bayesian network inference is equal to the number of variables in a network, which in the networks considered in this pap... |

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Citation Context ...sampling (Shachter & Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (=-=Heckerman, Horvitz, & Nathwani, 1990-=-), and the ANDES network (Conati, Gertner, VanLehn, & Druzdzel, 1997), with evidence as unlikely as 10 −41 . While the AIS-BN algorithm always performed better than the other two algorithms, in the ma... |

14 | Computational investigation of low-discrepancy sequences in simulation algorithms for Bayesian networks - Cheng, Druzdzel - 2000 |

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Citation Context ...urately enough, we can use this new network to solve other approximate tasks, such as the problem of computing the Maximum A-Posterior assignment (MAP) (Pearl, 1988), finding k most likely scenarios (=-=Seroussi & Golmard, 1994-=-), etc. A large advantage of this approach is that we can solve each of these problems as if the network had no evidence nodes. We know that Markov blanket scoring can improve convergence rates in som... |

7 | Latin hypercube sampling in Bayesian networks - Cheng, Druzdzel - 2000 |

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Citation Context ...not used in practice as often as the simple likelihood weighting scheme. There are also some other simulation algorithms, such as bounded variance algorithm (Dagum & Luby, 1997) and the AA algorithm (=-=Dagum et al., 1995-=-), which are essentially based on the LW algorithm and the Stopping-Rule Theorem (Dagum et al., 1995). Cano et al. (1996) proposed another importance sampling algorithm that performed somewhat better ... |

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An algorithm directly the K most probable con in Bayesian networks
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Citation Context ...nough, we can use this new network to solve other approximate tasks, such as the problem of computing the Maximum A-Posterior assignment (MAP) (Pearl, 1988),snding k most likely scenarios (Seroussi & =-=Golmard, 1994-=-), etc. A large advantage of this approach is that we can solve each of these problems as if the network had no evidence nodes. We know that Markov blanket scoring can improve convergence rates in som... |