Another look at statistical inference with machine learning-imputed data
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.034 | 0.172 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.004 | 0.013 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".