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Demystifying Prediction Powered Inference

Yilin Song, Dan M. Kluger, Harsh Parikh, Tian Gu

TL;DR

The paper addresses the challenge of using machine learning predictions to augment statistical inference without sacrificing validity. It introduces Prediction-Powered Inference (PPI) as a principled framework that leverages predictions from large unlabeled datasets while applying a bias-correction term based on a smaller labeled subset, enabling efficiency gains when predictions are informative. The authors synthesize theoretical foundations, a unified view of PPI variants, and practical diagnostics, and provide a three-step workflow for operationalizing PPI in applied research. Empirical results on the MOSAIKS housing data show that PPI can yield tighter confidence intervals than complete-case analysis, but also reveal vulnerabilities to double-dipping and MNAR mechanisms, underscoring the need for design-based safeguards and careful variant selection. The work culminates in a decision flowchart, diagnostics, and a targeted summary of selective methods, positioning PPI as a versatile framework that unites methodological advances with applied practice for responsible integration of predictions into valid inference.

Abstract

Machine learning predictions are increasingly used to supplement incomplete or costly-to-measure outcomes in fields such as biomedical research, environmental science, and social science. However, treating predictions as ground truth introduces bias while ignoring them wastes valuable information. Prediction-Powered Inference (PPI) offers a principled framework that leverages predictions from large unlabeled datasets to improve statistical efficiency while maintaining valid inference through explicit bias correction using a smaller labeled subset. Despite its potential, the growing PPI variants and the subtle distinctions between them have made it challenging for practitioners to determine when and how to apply these methods responsibly. This paper demystifies PPI by synthesizing its theoretical foundations, methodological extensions, connections to existing statistics literature, and diagnostic tools into a unified practical workflow. Using the Mosaiks housing price data, we show that PPI variants produce tighter confidence intervals than complete-case analysis, but that double-dipping, i.e. reusing training data for inference, leads to anti-conservative confidence intervals and coverages. Under missing-not-at-random mechanisms, all methods, including classical inference using only labeled data, yield biased estimates. We provide a decision flowchart linking assumption violations to appropriate PPI variants, a summary table of selective methods, and practical diagnostic strategies for evaluating core assumptions. By framing PPI as a general recipe rather than a single estimator, this work bridges methodological innovation and applied practice, helping researchers responsibly integrate predictions into valid inference.

Demystifying Prediction Powered Inference

TL;DR

The paper addresses the challenge of using machine learning predictions to augment statistical inference without sacrificing validity. It introduces Prediction-Powered Inference (PPI) as a principled framework that leverages predictions from large unlabeled datasets while applying a bias-correction term based on a smaller labeled subset, enabling efficiency gains when predictions are informative. The authors synthesize theoretical foundations, a unified view of PPI variants, and practical diagnostics, and provide a three-step workflow for operationalizing PPI in applied research. Empirical results on the MOSAIKS housing data show that PPI can yield tighter confidence intervals than complete-case analysis, but also reveal vulnerabilities to double-dipping and MNAR mechanisms, underscoring the need for design-based safeguards and careful variant selection. The work culminates in a decision flowchart, diagnostics, and a targeted summary of selective methods, positioning PPI as a versatile framework that unites methodological advances with applied practice for responsible integration of predictions into valid inference.

Abstract

Machine learning predictions are increasingly used to supplement incomplete or costly-to-measure outcomes in fields such as biomedical research, environmental science, and social science. However, treating predictions as ground truth introduces bias while ignoring them wastes valuable information. Prediction-Powered Inference (PPI) offers a principled framework that leverages predictions from large unlabeled datasets to improve statistical efficiency while maintaining valid inference through explicit bias correction using a smaller labeled subset. Despite its potential, the growing PPI variants and the subtle distinctions between them have made it challenging for practitioners to determine when and how to apply these methods responsibly. This paper demystifies PPI by synthesizing its theoretical foundations, methodological extensions, connections to existing statistics literature, and diagnostic tools into a unified practical workflow. Using the Mosaiks housing price data, we show that PPI variants produce tighter confidence intervals than complete-case analysis, but that double-dipping, i.e. reusing training data for inference, leads to anti-conservative confidence intervals and coverages. Under missing-not-at-random mechanisms, all methods, including classical inference using only labeled data, yield biased estimates. We provide a decision flowchart linking assumption violations to appropriate PPI variants, a summary table of selective methods, and practical diagnostic strategies for evaluating core assumptions. By framing PPI as a general recipe rather than a single estimator, this work bridges methodological innovation and applied practice, helping researchers responsibly integrate predictions into valid inference.
Paper Structure (31 sections, 12 equations, 4 figures, 3 tables)

This paper contains 31 sections, 12 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Prediction-Powered Inference: Framework and Extensions
  3. Basic setup and estimator
  4. Core assumptions and efficiency intuition
  5. A unified view of PPI variants
  6. Efficiency-guaranteeing refinements
  7. Robustness to labeling mechanism and accounting for distribution shift
  8. Beyond pre-trained model
  9. Handling missingness patterns
  10. Theoretical Connections with Statistics Literature
  11. Semiparametric efficiency and doubly robust estimation
  12. Control variates, survey sampling approaches, and finite-sample limits
  13. Bayesian inference
  14. Data integration and transfer learning
  15. Operationalizing PPI
  16. ...and 16 more sections

Figures (4)

  • Figure 1: Overall workflow of the practical guide of using PPI.
  • Figure 2: Decision flowchart for selecting PPI variants based on assumption diagnostics.
  • Figure 3: Estimates and average 90% confidence interval length for linear regression coefficients in Mosaiks housing data. The verticle line indicates the true coefficient values.
  • Figure 4: MNAR assessment. The vertical line indicates the true coefficient values.