# Importance Sampling with Unequal Support

arXiv: https://arxiv.org/abs/1611.03451 · HTML: https://mlsanity.com/paper/1611.03451/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2016.

## Built on by (most cited first, 5 of 5)

- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [FLAG: Flow Policy MaxEnt-RL by Latent Augmented Guidance](https://mlsanity.com/paper/2605.30749/) (2026)
- [Regularizing Extrapolation in Causal Inference](https://mlsanity.com/paper/2509.17180/) (2025)
- [A/B testing under Interference with Partial Network Information](https://mlsanity.com/paper/2404.10547/) (2024)
- [When Does Action Credit Need Updating?](https://mlsanity.com/paper/2609.29007/) (2026)

## Abstract (arXiv)

Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance sampling-based estimates by orders of magnitude when the supports of the training and testing distributions differ. After motivating and presenting our new importance sampling estimator, we provide a detailed theoretical analysis that characterizes both its bias and variance relative to the ordinary importance sampling estimator (in various settings, which include cases where ordinary importance sampling is biased, while our new estimator is not, and vice versa). We conclude with an example of how our new importance sampling estimator can be used to improve estimates of how well a new treatment policy for diabetes will work for an individual, using only data from when the individual used a previous treatment policy.