# PPI is the Difference Estimator: Recognizing the Survey Sampling Roots of Prediction-Powered Inference

arXiv: https://arxiv.org/abs/2603.19160 · HTML: https://mlsanity.com/paper/2603.19160/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [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)
- [More power to you: Using machine learning to augment human coding for more efficient inference in text-based randomized trials](https://mlsanity.com/paper/2309.13666/) (2023)
- [Stratified Sampling for Model-Assisted Estimation with Surrogate Outcomes](https://mlsanity.com/paper/2602.12992/) (2026)
- [Optimal allocation of sample size for randomization-based inference from 2K factorial designs](https://mlsanity.com/paper/2306.12394/) (2023)

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

- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Prediction-Powered Inference Across Many Tasks for AI Evaluation & Social Science Research](https://mlsanity.com/paper/2605.29249/) (2026)
- [Allocating Human Oversight in AI-Enabled Analytics](https://mlsanity.com/paper/2604.12497/) (2026)
- [Beyond the Training Distribution: Evaluating Predictions Under Distribution Shift and Selection Bias](https://mlsanity.com/paper/2606.14506/) (2026)
- [proxymate: Diagnosis and Adjustment of Proxy Estimates for Reliable Inference](https://mlsanity.com/paper/2607.24401/) (2026)
- [Prediction-Powered Smoothing and Validation for Disaggregated AI Evaluation](https://mlsanity.com/paper/2609.20758/) (2026)
- [Cluster-Robust Prediction-Powered Inference](https://mlsanity.com/paper/2610.09601/) (2026)

## Abstract (arXiv)

Prediction-powered inference (PPI) is a rapidly growing framework for combining machine learning predictions with a small set of gold-standard labels to conduct valid statistical inference. In this article, I argue that the core estimators underlying PPI are equivalent to well-established estimators from the survey sampling literature dating back to the 1970s. Specifically, the PPI estimator for a population mean is algebraically equivalent to the difference estimator of Cassel et al. (1976), and PPI plus corresponds to the generalized regression (GREG) estimator of Sarndal et al. (2003). Recognizing this equivalence, I consider what part of PPI is inherited from a long-standing literature in statistics, what part is genuinely new, and where inferential claims require care. After introducing the two frameworks and establishing their equivalence, I break down where PPI diverges from model-assisted estimation, including differences in the mode of inference, the role of the unlabeled data pool, and the consequences of differential prediction error for subgroup estimands such as the average treatment effect. I then identify what each framework offers the other: PPI researchers can draw on the survey sampling literature's well-developed theory of calibration, optimal allocation, and design-based diagnostics, while survey sampling researchers can benefit from PPI's extensions to non-standard estimands and its accessible software ecosystem. The article closes with a call for integration between these two communities, motivated by the growing use of large language models as measurement instruments in applied research.