# Imputation-Powered Inference

arXiv: https://arxiv.org/abs/2509.13778 · HTML: https://mlsanity.com/paper/2509.13778/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [Cross-validation Confidence Intervals for Test Error](https://mlsanity.com/paper/2007.12671/) (2020)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [Prediction-Powered Inference with Imputed Covariates and Nonuniform Sampling](https://mlsanity.com/paper/2501.18577/) (2025)
- [Multiple Imputation: A Review of Practical and Theoretical Findings](https://mlsanity.com/paper/1801.04058/) (2018)
- [Prediction De-Correlated Inference: A safe approach for post-prediction inference](https://mlsanity.com/paper/2312.06478/) (2023)
- [A Note on the Prediction-Powered Bootstrap](https://mlsanity.com/paper/2405.18379/) (2024)
- [Another look at statistical inference with machine learning-imputed data](https://mlsanity.com/paper/2411.19908/) (2024)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Modular Regression: Improving Linear Models by Incorporating Auxiliary Data](https://mlsanity.com/paper/2211.10032/) (2022)
- [On Inverse Probability Weighting for Nonmonotone Missing at Random Data](https://mlsanity.com/paper/1411.5310/) (2014)
- [Adaptive and Efficient Learning with Blockwise Missing and Semi-Supervised Data](https://mlsanity.com/paper/2405.18722/) (2024)
- [Bootstrap Inference for Multiple Imputation under Uncongeniality and Misspecification](https://mlsanity.com/paper/1911.09980/) (2019)

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

- [Demystifying Prediction Powered Inference](https://mlsanity.com/paper/2601.20819/) (2026)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Valid Inference with Synthetic Data via Task Exchangeability](https://mlsanity.com/paper/2606.13629/) (2026)
- [Testing hypotheses via orthogonalization](https://mlsanity.com/paper/2606.29732/) (2026)
- [Assumption-lean logistic regression with missing covariates](https://mlsanity.com/paper/2610.07292/) (2026)

## Abstract (arXiv)

Modern multi-modal and multi-site data frequently suffer from blockwise missingness, where subsets of features are missing for groups of individuals, creating complex patterns that challenge standard inference methods. Existing approaches have critical limitations: complete-case analysis discards informative data and is potentially biased; doubly robust estimators for non-monotone missingness-where the missingness patterns are not nested subsets of one another-can be theoretically efficient but lack closed-form solutions and often fail to scale; and blackbox imputation can leverage partially observed data to improve efficiency but provides no inferential guarantees when misspecified. To address the limitations of these existing methods, we propose imputation-powered inference (IPI), a model-lean framework that combines the flexibility of blackbox imputation with bias correction using fully observed data, drawing on ideas from prediction-powered inference and semiparametric inference. IPI enables valid and efficient M-estimation under missing completely at random (MCAR) blockwise missingness and improves subpopulation inference under a weaker assumption we formalize as first-moment MCAR, for which we also provide practical diagnostics. Simulation studies and a clinical application demonstrate that IPI may substantially improve subpopulation efficiency relative to complete-case analysis, while maintaining statistical validity in settings where both doubly robust estimators and naive imputation fail to achieve nominal coverage.