Monte Carlo Inference via Greedy Importance Sampling
This work addresses variance reduction in probabilistic inference for researchers in machine learning and statistics, but it is incremental as it extends prior one-dimensional results to broader applications.
The authors tackled the problem of high variance in Monte Carlo inference for graphical models by combining explicit search with importance sampling, proving unbiasedness and demonstrating improved inference quality over standard MCMC methods like Gibbs and Metropolis 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.