Prediction-Powered Inference (PPI) was introduced in 2023 as a method for combining machine learning predictions with labeled data to estimate population quantities. The idea: use a large unlabeled dataset scored by a predictive model, then correct the model's systematic errors using a smaller labeled validation set.
This paper shows that PPI is algebraically equivalent to the difference estimator of Cassel, Särndal, and Swensson (1976). PPI++ — the improved variant with a tuning parameter — is equivalent to the generalized regression (GREG) estimator. Both were developed in survey sampling theory fifty years ago.
The correspondence is exact, not approximate. The same formula, the same variance reduction mechanism, the same optimality properties. The survey sampling literature derived these estimators for combining auxiliary information (census data, administrative records) with probability samples. PPI rediscovered them for combining model predictions with labeled data. The mathematical structure is identical because the statistical problem is identical: you have an imperfect proxy for the quantity of interest and a smaller dataset that lets you measure the proxy's error.
The paper's tone is constructive rather than dismissive. Both communities benefit from recognizing the connection. PPI researchers gain access to decades of theory on calibration, post-stratification, and non-response adjustment. Survey statisticians gain access to PPI's extensions to new problem types and its software ecosystem.
But the deeper lesson is about disciplinary amnesia. A foundational technique can be reinvented from scratch, published in top venues, and widely adopted — all without anyone noticing it already existed in an adjacent field. The barrier to recognizing prior work is not obscurity but vocabulary. The same idea dressed in different notation becomes invisible.