David Broska, Michael Howes
arXiv 7 Oct 2026 · Statistics — Methodology
arXiv:2610.09601 · PDF · Extracted main text
Data collection is often costly or logistically demanding, limiting both the questions researchers can pursue and how precisely they can answer them. Prediction-powered inference (PPI) can reduce the amount of data needed for precise parameter estimation by combining labeled data with machine learning predictions. However, ignoring dependence within clusters can produce confidence intervals that cover the true parameter less often than their nominal rate. We introduce Cluster-Robust PPI++, which provides standard errors in closed form and asymptotically valid confidence intervals under arbitrary dependence within independent clusters, requiring no bootstrap or resampling. Our central contribution is to accommodate partially labeled clusters, a common empirical setting in which clusters contain both labeled and unlabeled units. As units are dependent within clusters, partially labeled clusters violate the independence assumption of PPI++. We also show how precision increases depend on the labeling design, and derive a cluster-aware power tuning rule that minimizes asymptotic variance. In an application to television news, standard PPI++ confidence intervals have coverage below 60%, whereas Cluster-Robust PPI++ can achieve nominal 95% coverage.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Angelopoulos, A. N., Duchi, J. C., and Zrnic, T (2024) PPI++: Efficient prediction-powered inference | 0.897 | 18 | 4 | 72% |
| 2 | Broska, D., Howes, M., and van Loon, A (2025) The mixed subjects design: Treating large language models as potentially informative observations self | 0.737 | 3 | 2 | 100% |
| 3 | Boussalis, C., Coan, T. G., Holman, M. R., and Müller, S (2021) Gender, candidate emotional expression, and voter reactions during televised debates | 0.644 | 2 | 2 | 100% |
| 4 | Rister Portinari Maranca, A., Chung, J., Hinck, M., Wolsky, A. D., E… (2025) Correcting the measurement errors of AI-assisted labeling in image analysis using design-based supervised learning | 0.644 | 2 | 2 | 100% |
| 5 | Girbau, A., Kobayashi, T., Renoust, B., Matsui, Y., and Satoh, S (2024) Face detection, tracking, and classification from large-scale news archives for analysis of key political figures | 0.511 | 2 | 2 | 50% |
| 6 | Kluger, D. M., Lu, K., Zrnic, T., Wang, S., and Bates, S (2025) Prediction-powered inference with imputed covariates and nonuniform sampling | 0.511 | 2 | 1 | 100% |
| 7 | Angelopoulos, A. N., Bates, S., Fannjiang, C., Jordan, M. I., and Zr… (2023) Prediction-powered inference | 0.405 | 1 | 1 | 100% |
| 8 | Arel-Bundock, V., Briggs, R. C., Doucouliagos, H., Aviña, M. M., and… (2026) Quantitative political science research is greatly underpowered | 0.405 | 1 | 1 | 100% |
| 9 | Cameron, A. C. and Miller, D. L (2015) A practitioner's guide to cluster-robust inference | 0.405 | 1 | 1 | 100% |
| 10 | Egami, N., Hinck, M., Stewart, B. M., and Wei, H (2023) Using imperfect surrogates for downstream inference: Design-based supervised learning for social science applications of large l… | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 24 scored citations.