# Another look at statistical inference with machine learning-imputed data

arXiv: https://arxiv.org/abs/2411.19908 · HTML: https://mlsanity.com/paper/2411.19908/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 65 references that are in the map.
- First posted on arXiv 29 Nov 2024.

## Builds on (most cited first, 20 of 20)

- [GatorTron: A Large Clinical Language Model to Unlock Patient Information from Unstructured Electronic Health Records](https://mlsanity.com/paper/2203.03540/) (2022)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [AutoEval Done Right: Using Synthetic Data for Model Evaluation](https://mlsanity.com/paper/2403.07008/) (2024)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Can Unconfident LLM Annotations Be Used for Confident Conclusions?](https://mlsanity.com/paper/2408.15204/) (2024)
- [Using Imperfect Surrogates for Downstream Inference: Design-based Supervised Learning for Social Science Applications of Large Language Models](https://mlsanity.com/paper/2306.04746/) (2023)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Prediction De-Correlated Inference: A safe approach for post-prediction inference](https://mlsanity.com/paper/2312.06478/) (2023)
- [Task-Agnostic Machine-Learning-Assisted Inference](https://mlsanity.com/paper/2405.20039/) (2024)
- [From Narratives to Numbers: Valid Inference Using Language Model Predictions from Verbal Autopsy Narratives](https://mlsanity.com/paper/2404.02438/) (2024)
- [Bayesian Prediction-Powered Inference](https://mlsanity.com/paper/2405.06034/) (2024)
- [Revisiting inference after prediction](https://mlsanity.com/paper/2306.13746/) (2023)
- [Do We Really Even Need Data?](https://mlsanity.com/paper/2401.08702/) (2024)
- [A Semiparametric Approach for Robust and Efficient Learning with Biobank Data](https://mlsanity.com/paper/2404.01191/) (2024)

## Built on by (most cited first, 7 of 7)

- [Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards](https://mlsanity.com/paper/2506.16658/) (2025)
- [A Unified Framework for Inference with General Missingness Patterns and Machine Learning Imputation](https://mlsanity.com/paper/2508.15162/) (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)
- [Spatially Robust Inference with Predicted and Missing at Random Labels](https://mlsanity.com/paper/2603.11368/) (2026)
- [Prediction-Powered Inference Across Many Tasks for AI Evaluation & Social Science Research](https://mlsanity.com/paper/2605.29249/) (2026)
- [When Surveys Become Conversations: Adaptive Matrix Validation for AI-Assisted Interviews](https://mlsanity.com/paper/2606.24244/) (2026)

## Abstract (arXiv)

From structural biology to epidemiology, predictions from machine learning (ML) models increasingly complement costly gold-standard data, enabling faster, more affordable, and scalable scientific inquiry. In response, prediction-based (PB) inference has emerged to support statistical analysis that combines a large volume of predicted data with a small amount of gold-standard data. The goals of PB inference are twofold: (i) to mitigate bias arising from prediction error and (ii) to improve efficiency relative to classical inference based solely on gold-standard data. While early PB inference methods primarily focused on bias mitigation, improving efficiency remains an active area of research. Motivated by connections between PB inference and longstanding problems in statistics and related fields, we draw on the two-phase sampling literature to introduce an approach for Z-estimation with ML-imputed outcomes that is guaranteed to match or exceed the efficiency of classical inference, regardless of prediction quality. We demonstrate the utility of our approach through theoretical and numerical analyses as well as an application to UK Biobank data. We further establish new connections between existing PB inference approaches and foundational and contemporary statistical methods.