Cycle-cutset sampling for Bayesian networks

作者: Bozhena Bidyuk , Rina Dechter

DOI: 10.1007/3-540-44886-1_23

关键词: Gibbs samplingComputer scienceSampling methodologySampling (statistics)Pattern recognitionMean squared errorSampling designBayesian networkErgodic theoryAlgorithmArtificial intelligenceSlice samplingSimple random sampleErgodicityImportance samplingVariance reduction

摘要: The paper presents a new sampling methodology for Bayesian networks called cutset that samples only subset of the variables and applies exact inference others. We show this approach can be implemented efficiently when sampled constitute cycle-cutset network otherwise it is exponential in induced-width network's graph, whose are removed. Cutset an instance well known Rao-Blakwellisation technique variance reduction investigated [5, 2, 16]. Moreover, proposed scheme extends standard methods to non-ergodic with ergodic subspaces. Our empirical results confirm those expectations cycle superior Gibbs variety benchmarks, yielding simple, yet powerful scheme.

参考文章(19)
Kristian G. Olesen, Finn V. Jensen, Steffen L. Lauritzen, Bayesian updating in causal probabilistic networks by local computations Computational Statistics Quarterly. ,vol. 4, pp. 269- 282 ,(1990)
Uffe Kjærulff, HUGS: combining exact inference and Gibbs sampling in junction trees uncertainty in artificial intelligence. pp. 368- 375 ,(1995)
D. J. C. Mackay, Introduction to Monte Carlo methods Proceedings of the NATO Advanced Study Institute on Learning in graphical models. pp. 175- 204 ,(1998) , 10.1007/978-94-011-5014-9_7
Yair Weiss, Kevin P. Murphy, Michael I. Jordan, Loopy belief propagation for approximate inference: an empirical study uncertainty in artificial intelligence. pp. 467- 475 ,(1999)
S. L. Lauritzen, D. J. Spiegelhalter, Local computations with probabilities on graphical structures and their application to expert systems Journal of the royal statistical society series b-methodological. ,vol. 50, pp. 415- 448 ,(1990) , 10.1111/J.2517-6161.1988.TB01721.X
Dan Geiger, Reuven Bar-Yehuda, Ann Becker, Random algorithms for the loop cutset problem uncertainty in artificial intelligence. pp. 49- 56 ,(1999)
Rina Dechter, Bucket elimination: A unifying framework for reasoning Artificial Intelligence. ,vol. 113, pp. 41- 85 ,(1999) , 10.1016/S0004-3702(99)00059-4
Stuart Geman, Donald Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. PAMI-6, pp. 721- 741 ,(1984) , 10.1109/TPAMI.1984.4767596
Uri Lerner, Daphne Koller, Dragomir Angelov, A general algorithm for approximate inference and its application to hybrid bayes nets uncertainty in artificial intelligence. pp. 324- 333 ,(1999)
George Casella, Christian P Robert, Rao-Blackwellisation of sampling schemes Biometrika. ,vol. 83, pp. 81- 94 ,(1996) , 10.1093/BIOMET/83.1.81