Monte Carlo inference via greedy importance sampling

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

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

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

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

[5]  R. M. Dudley,et al.  Real Analysis and Probability , 1989 .

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

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

[8]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[9]  M. Evans.  Chaining Via Annealing , 1991 .

[10]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..

[11]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[12]  Remco R. Bouckaert,et al.  A Stratified Simulation Scheme for Inference in Bayesian Belief Networks , 1994, UAI.

[13]  Robert M. Fung,et al.  Backward Simulation in Bayesian Networks , 1994, UAI.

[14]  Stuart J. Russell,et al.  Stochastic simulation algorithms for dynamic probabilistic networks , 1995, UAI.

[15]  Geoffrey E. Hinton,et al.  Bayesian Learning for Neural Networks , 1995 .

[16]  Serafín Moral,et al.  Importance sampling algorithms for the propagation of probabilities in belief networks , 1996, Int. J. Approx. Reason..

[17]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[18]  Michael Isard,et al.  Contour Tracking by Stochastic Propagation of Conditional Density , 1996, ECCV.

[19]  Michael Luby,et al.  An Optimal Approximation Algorithm for Bayesian Inference , 1997, Artif. Intell..

[20]  Brendan J. Frey,et al.  Graphical Models for Machine Learning and Digital Communication , 1998 .

[21]  Dale Schuurmans,et al.  Greedy Importance Sampling , 1999, NIPS.

[22]  Dudley,et al.  Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .