# Prediction-Powered Inference with Inverse Probability Weighting

arXiv: https://arxiv.org/abs/2508.10149 · HTML: https://mlsanity.com/paper/2508.10149/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [A Generalizable and Accessible Approach to Machine Learning with Global Satellite Imagery](https://mlsanity.com/paper/2010.08168/) (2020)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [A Deep Learning Approach for Population Estimation from Satellite Imagery](https://mlsanity.com/paper/1708.09086/) (2017)
- [Adaptive normalization for IPW estimation](https://mlsanity.com/paper/2106.07695/) (2021)
- [A note on the consistency of the Narain-Horvitz-Thompson estimator](https://mlsanity.com/paper/1412.2887/) (2014)
- [Quantile Importance Sampling](https://mlsanity.com/paper/2305.03158/) (2023)

## Built on by (most cited first, 3 of 3)

- [Revisiting Active Sequential Prediction-Powered Mean Estimation](https://mlsanity.com/paper/2604.18569/) (2026)
- [When Can You Trust Your Synthetic Users? Diagnostics and Corrections for LLM Consumer Panels](https://mlsanity.com/paper/2609.13148/) (2026)
- [OTROPE: Optimal Transport-based Robust Off-policy Evaluation for Large Language Models](https://mlsanity.com/paper/2609.36264/) (2026)

## Abstract (arXiv)

Prediction-powered inference (PPI) is a recent framework for valid statistical inference with partially labeled data, combining model-based predictions on a large unlabeled set with bias correction from a smaller labeled subset. Building on existing PPI results under covariate shift, we show that PPI rectification admits a direct design-based interpretation, and that informative labeling can be handled naturally by Horvitz--Thompson and H'ajek-style corrections. This connection unites design-based survey sampling ideas with modern prediction-assisted inference, yielding estimators that remain valid when labeling probabilities vary across units. We consider the common setting where the inclusion probabilities are not known but estimated from a correctly specified model. In simulations, the performance of IPW-adjusted PPI with estimated propensities closely matches the known-probability case, retaining both nominal coverage and the variance-reduction benefits of PPI.