# Adaptive Importance Sampling for Estimation in Structured Domains

arXiv: https://arxiv.org/abs/1301.3882 · HTML: https://mlsanity.com/paper/1301.3882/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [Contrastive Continual Learning with Importance Sampling and Prototype-Instance Relation Distillation](https://mlsanity.com/paper/2403.04599/) (2024)
- [Massively Parallel Expectation Maximization For Approximate Posteriors](https://mlsanity.com/paper/2503.08264/) (2025)

## Abstract (arXiv)

Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important 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 minization of the variance. We also present other stochastic-gradient-descent methods based on the minimizationof 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.