Adaptive Importance Sampling for Estimation in Structured Domains

Sampling is an important tool for estimating large, complex sums and integrals over highdimensional spaces. For instance, importance sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we want to have a sampling distribution that provides optimal-variance estimators. In this paper, we present methods that improve the sampling distribution by systematically adapting it as we obtain information from the samples. We present a stochastic-gradient-descent method for sequentially updating the sampling distribution based on the direct minimization of the variance. We also present other stochastic-gradient-descent methods based on the minimization of typical notions of distance between the current sampling distribution and approximations of the target, optimal distribution. We finally validate and compare the different methods empirically by applying them to the problem of action evaluation in influence diagrams.

• Type: Conference
• Year: 2000
• Where: UAI
• Authors: Luis E. Ortiz, Leslie Pack Kaelbling
• Keywords: Current Sampling Distribution, Importance Sampling, Sampling Distribution, UAI 2000, UAI 2008