Latin Hypercube Sampling in Bayesian Networks

We propose a scheme for producing Latin hypercube samples that can enhance any of the existing sampling algorithms in Bayesian networks. We test this scheme in combination with the likelihood weighting algorithm and show that it can lead to a significant improvement in the convergence rate. While performance of sampiing algorithms in general depends on the numerical properties of a network, in our experiments Latin hypercube sampling performed always better than random sampling. In some cases we observed as much as an order of magnitude improvement in convergence rates. We discuss practical issues related to storage requirements of Latin hypercube sample generation and propose a low-storage, anytime cascaded version of Latin hypercube sampling that introduces a minimal performance loss compared to the original scheme. 1

[1]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[2]  Cristina Conati,et al.  On-Line Student Modeling for Coached Problem Solving Using Bayesian Networks , 1997 .

[3]  M. Stein.  Large sample properties of simulations using latin hypercube sampling , 1987 .

[4]  Gregory M. Provan,et al.  Knowledge Engineering for Large Belief Networks , 1994, UAI.

[5]  李幼升,et al.  Ph , 1989 .

[6]  Mark E. Frisse,et al.  A tutorial introduction to stochastic simulation algorithms for belief networks , 1993, Artif. Intell. Medicine.

[7]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[8]  Kuo-Chu Chang,et al.  Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks , 2013, UAI.

[9]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[10]  Ross D. Shachter,et al.  Simulation Approaches to General Probabilistic Inference on Belief Networks , 2013, UAI.

[11]  B. Efron,et al.  The Jackknife Estimate of Variance , 1981 .

[12]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[13]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

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

[15]  R. Martin Chavez,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Gregory F. Cooper,et al.  NESTOR: A Computer-Based Medical Diagnostic Aid That Integrates Causal and Probabilistic Knowledge. , 1984 .