AND/OR Importance Sampling

The paper introduces AND/OR importance sampling for probabilistic graphical models. In contrast to importance sampling, AND/OR importance sampling caches samples in the AND/OR space and then extracts a new sample mean from the stored samples. We prove that AND/OR importance sampling may have lower variance than importance sampling; thereby providing a theoretical justification for preferring it over importance sampling. Our empirical evaluation demonstrates that AND/OR importance sampling is far more accurate than importance sampling in many cases.

[1]  Rina Dechter,et al.  An Empirical Study of w-Cutset Sampling for Bayesian Networks , 2003, UAI.

[2]  Uffe Kjærulff.  HUGS: Combining Exact Inference and Gibbs Sampling in junction Trees , 1995, UAI.

[3]  Augustine Kong,et al.  The properties of the cross-match estimate and split sampling , 1997 .

[4]  Jian Cheng,et al.  AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks , 2000, J. Artif. Intell. Res..

[5]  Steffen L. Lauritzen,et al.  Hybrid Propagation in Junction Trees , 1994, IPMU.

[6]  Rina Dechter,et al.  AND/OR search spaces for graphical models , 2007, Artif. Intell..

[7]  S. Moral,et al.  Mixing exact and importance sampling propagation algorithms in dependence graphs , 1997 .

[8]  Dan Geiger,et al.  Optimizing exact genetic linkage computations , 2003, RECOMB '03.

[9]  Mark A. Paskin.  Sample Propagation , 2003, NIPS.

[10]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[11]  Changhe Yuan,et al.  Importance sampling algorithms for Bayesian networks: Principles and performance , 2006, Math. Comput. Model..

[12]  Vibhav Gogate,et al.  SampleSearch: A Scheme that Searches for Consistent Samples , 2007, AISTATS.

[13]  Vibhav Gogate,et al.  Approximate Inference Algorithms for Hybrid Bayesian Networks with Discrete Constraints , 2005, UAI.

[14]  Serafín Moral,et al.  Mixing exact and importance sampling propagation algorithms in dependence graphs , 1997, Int. J. Intell. Syst..

[15]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .