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...

As Bayesian networks are applied to more complex and realistic real-world applications, the development of more efficient inference algorithms working under real-time constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network inference algorithms. In particular, previous research on real-time inference is reviewed. It provides a framework for understanding these algorithms and the relationships between them. Some important issues in real-time Bayesian networks inference are also discussed.

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In this paper, we investigate the application of the ideas behind Lazy propagation to the Penniless propagation scheme. In addition to the use of probability trees to represent and approximate potentials, both in the messages and in the nodes of the join tree, those potentials are not combined to obtain the joint potential over a node of the join tree or over a message. Rather, those joint potentials are represented in a factorized way, and the combinations are postponed until they are compulsory for the deletion of a variable. Here we test two variations of the basic Lazy scheme. One is based in keeping a hash table of combined potentials so that computations are not repeated. The other one consists in using heuristics to determine an order of combination of a list of potentials.

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant points in the target distribution. We prove that it is possible to introduce search and still maintain unbiasedness. We then demonstrate our procedure on a few simple inference tasks and show that it can improve the inference quality of standard MCMC methods, including Gibbs sampling, Metropolis sampling, and Hybrid Monte Carlo. This paper extends previous work which showed how greedy importance sampling could be correctly realized in the one-dimensional case. 1 Introduction It is well known that general inference and learning with Bayesian networks is computationally hard [DL93, Rot93], and it is therefore necessary to consider restricted architectures [Pea88], or heuristic and approximate algorithms to perform these tasks [JGJS98, Fre9...

A class of Monte Carlo algorithms for probability propagation in belief networks is given. The simulation is based on a two steps procedure. The first one is a node deletion technique to calculate the 'a posteriori' distribution on a variable, with the particularity that when exact computations are too costly, they are carried out in an approximate way. In the second step, the computations done in the first one are used to obtain random configurations for the variables of interest. These configurations are weighted according to the importance sampling methodology. Different particular algorithms are obtained depending on the approximation procedure used in the first step and in the way of obtaining the random configurations. In this last case, a stratified sampling technique is used, which has been adapted to be applied to very large networks without problems with rounding errors.