Principles of artificial intelligence
Principles of artificial intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
A general scheme for automatic generation of search heuristics from specification dependencies
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Optimizing exact genetic linkage computations
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Hybrid Propagation in Junction Trees
IPMU'94 Selected papers from the 5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems, Advances in Intelligent Computing
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
AND/OR search spaces for graphical models
Artificial Intelligence
On probabilistic inference by weighted model counting
Artificial Intelligence
Approximate Solution Sampling (and Counting) on AND/OR Spaces
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
And/or search strategies for combinatorial optimization in graphical models
And/or search strategies for combinatorial optimization in graphical models
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Approximate counting by sampling the backtrack-free search space
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Cutset sampling for Bayesian networks
Journal of Artificial Intelligence Research
From sampling to model counting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Dynamic importance sampling in Bayesian networks based on probability trees
International Journal of Approximate Reasoning
Sampling algorithms for probabilistic graphical models with determinism
Sampling algorithms for probabilistic graphical models with determinism
International Journal of Approximate Reasoning
Join-graph propagation algorithms
Journal of Artificial Intelligence Research
SampleSearch: Importance sampling in presence of determinism
Artificial Intelligence
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Iterative join-graph propagation
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
HUGS: combining exact inference and Gibbs sampling in junction trees
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Value elimination: bayesian inference via backtracking search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
An importance sampling algorithm based on evidence pre-propagation
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Importance sampling algorithms for Bayesian networks: Principles and performance
Mathematical and Computer Modelling: An International Journal
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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It is well known that the accuracy of importance sampling can be improved by reducing the variance of its sample mean and therefore variance reduction schemes have been the subject of much research. In this paper, we introduce a family of variance reduction schemes that generalize the sample mean from the conventional OR search space to the AND/OR search space for graphical models. The new AND/OR sample means allow trading time and space with variance. At one end is the AND/OR sample tree mean which has the same time and space complexity as the conventional OR sample tree mean but has smaller variance. At other end is the AND/OR sample graph mean which requires more time and space to compute but has the smallest variance. Theoretically, we show that the variance is smaller in the AND/OR space because the AND/OR sample mean is defined over a larger virtual sample size compared with the OR sample mean. Empirically, we demonstrate that the AND/OR sample mean is far closer to the true mean than the OR sample mean.