# Prediction-Powered Inference with Imputed Covariates and Nonuniform Sampling

arXiv: https://arxiv.org/abs/2501.18577 · HTML: https://mlsanity.com/paper/2501.18577/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 19 of 19)

- [Demystifying Prediction Powered Inference](https://mlsanity.com/paper/2601.20819/) (2026)
- [A Unified Framework for Inference with General Missingness Patterns and Machine Learning Imputation](https://mlsanity.com/paper/2508.15162/) (2025)
- [Benchmarking Debiasing Methods for LLM-based Parameter Estimates](https://mlsanity.com/paper/2506.09627/) (2025)
- [Robust Sampling for Active Statistical Inference](https://mlsanity.com/paper/2511.08991/) (2025)
- [Imputation-Powered Inference](https://mlsanity.com/paper/2509.13778/) (2025)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Generalized Prediction-Powered Inference, with Application to Binary Classifier Evaluation](https://mlsanity.com/paper/2602.10332/) (2026)
- [Augmented transfer regression learning for completely missing covariates](https://mlsanity.com/paper/2605.04469/) (2026)
- [Industrializing Prediction-Powered Inference: The GLIDE Library for Reliable GenAI and Agentic Systems Evaluation](https://mlsanity.com/paper/2605.31278/) (2026)
- [Optimized Labeling Resource Allocation for Prediction-Assisted Inference via OPAL](https://mlsanity.com/paper/2606.03211/) (2026)
- [Valid Inference with Synthetic Data via Task Exchangeability](https://mlsanity.com/paper/2606.13629/) (2026)
- [Empirical Bayes Rebiasing](https://mlsanity.com/paper/2605.08069/) (2026)
- [Learning U-Statistics with Active Inference](https://mlsanity.com/paper/2605.11638/) (2026)
- [proxymate: Diagnosis and Adjustment of Proxy Estimates for Reliable Inference](https://mlsanity.com/paper/2607.24401/) (2026)
- [Doubly robust target inference for generalized linear regression with completely missing covariates](https://mlsanity.com/paper/2609.24086/) (2026)
- [ABC-Align: Prediction-Powered Alignment with Adaptive Bias Control](https://mlsanity.com/paper/2609.34374/) (2026)
- [Assumption-lean logistic regression with missing covariates](https://mlsanity.com/paper/2610.07292/) (2026)
- [Prediction-powered inference for time series across space](https://mlsanity.com/paper/2610.08715/) (2026)
- [Cluster-Robust Prediction-Powered Inference](https://mlsanity.com/paper/2610.09601/) (2026)

## Abstract (arXiv)

Machine learning models are increasingly used to produce predictions that serve as input data in subsequent statistical analyses. For example, computer vision predictions of economic and environmental indicators based on satellite imagery are used in downstream regressions; similarly, language models are widely used to approximate human ratings and opinions in social science research. However, failure to properly account for errors in the machine learning predictions renders standard statistical procedures invalid. Prior work uses what we call the Predict-Then-Debias estimator to give valid confidence intervals when machine learning algorithms impute missing variables, assuming a small complete sample from the population of interest. We expand the scope by introducing bootstrap confidence intervals that apply when the complete data is a nonuniform (i.e., weighted, stratified, or clustered) sample and to settings where an arbitrary subset of features is imputed. Importantly, the method can be applied to many settings without requiring additional calculations. We prove that these confidence intervals are valid under no assumptions on the quality of the machine learning model and are no wider than the intervals obtained by methods that do not use machine learning predictions.