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Prediction-Powered Adaptive Shrinkage Estimation
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Introduces Prediction-Powered Adaptive Shrinkage (PAS), which power-tunes PPI within each problem and then shrinks toward ML prediction means across many parallel mean-estimation problems, choosing the shrinkage by minimizing a correlation-aware unbiased risk estimate (CURE).
Problem
Estimating many parallel means (compound estimation) when gold-standard labels are scarce but ML predictions are available; existing PPI methods target single statistical problems and remain unbiased, leaving MSE gains on the table.
Approach
Combine within-problem power-tuned PPI (unbiased variance reduction) with across-problem empirical Bayes shrinkage toward the ML prediction mean, with a single global shrinkage parameter tuned by minimizing CURE, an unbiased estimate of compound risk that accounts for covariance between the shrinkage source and target.
Key results
- On the Amazon review task with tuned BERT predictor, PAS achieves MSE 3.287e-3 versus 24.305e-3 for the classical estimator and 6.289e-3 for PT, with 80.8% of problems improved.
- On the synthetic model with good predictor f1(x)=x^2, PAS matches the best MSE (0.272e-3, tied with shrink-classical) versus 3.142e-3 for classical; with flawed predictor f2, PAS gets 2.466e-3 vs 2.659e-3 for PT.
- On Galaxy Zoo 2 spiral fractions over 100 subgroups, PAS achieves the lowest MSE (0.893e-3) vs 2.073e-3 for classical and 1.026e-3 for PT, though shrink-average has the highest percent improved (68.9% vs 67.3%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add adaptive shrinkage to PT (ablation) | PAS · Synthetic, f1(x)=x² | MSE (× 10^-3): 2.642 ± 0.027 -> 0.272 ± 0.003 | Helped |
| Add power tuning to shrink-classical estimator (ablation) | PAS · Synthetic, f1(x)=x² | MSE (× 10^-3): 0.272 ± 0.003 -> 0.272 ± 0.003 | No clear effect |
| Add adaptive shrinkage to PT (ablation) | PAS · Synthetic, f2(x)=|x| | MSE (× 10^-3): 2.659 ± 0.026 -> 2.466 ± 0.026 | Helped |
| Add power tuning to shrink-classical estimator (ablation) | PAS · Synthetic, f2(x)=|x| | MSE (× 10^-3): 2.863 ± 0.030 -> 2.466 ± 0.026 | Helped |
| Add adaptive shrinkage to PT (ablation) | PAS · Amazon (base f; BERT-base) | MSE (× 10^-3): 10.633 ± 0.089 -> 8.517 ± 0.071 | Helped |
| Add power tuning to shrink-classical estimator (ablation) | PAS · Amazon (base f; BERT-base) | MSE (× 10^-3): 15.995 ± 0.121 -> 8.517 ± 0.071 | Helped |
| Add adaptive shrinkage to PT (ablation) | PAS · Amazon (tuned f; BERT-tuned) | MSE (× 10^-3): 6.289 ± 0.050 -> 3.287 ± 0.024 | Helped |
| Add power tuning to shrink-classical estimator (ablation) | PAS · Amazon (tuned f; BERT-tuned) | MSE (× 10^-3): 3.828 ± 0.039 -> 3.287 ± 0.024 | Helped |
| Add adaptive shrinkage to PT (ablation) | PAS · Galaxy Zoo 2 (WVT_BIN subgroups) | MSE (× 10^-3): 1.026 ± 0.015 -> 0.893 ± 0.011 | Helped |
| Add power tuning to shrink-classical estimator (ablation) | PAS · Galaxy Zoo 2 (WVT_BIN subgroups) | MSE (× 10^-3): 1.522 ± 0.016 -> 0.893 ± 0.011 | Helped |
Surprising findings
- Shrinking toward the raw prediction mean alone can reach near-optimal MSE when the predictor is good, while the prediction mean is badly biased for the flawed BERT-base predictor (MSE 41.3e-3 vs 24.3e-3 classical).
Limitations
- Theory assumes known second moments for the main PAS result; real-data experiments use sample-based estimates not covered by theory.
- Asymptotic optimality requires number of problems m to grow while per-problem sample sizes stay bounded.
- Focuses on point estimation; no coverage-controlling confidence intervals provided.
Experimental setup
Datasets: Amazon Fine Food Reviews Galaxy Zoo 2 synthetic Gaussian model
Benchmarks: synthetic model Amazon Fine Food Reviews Galaxy Zoo 2 spiral fractions
Metrics: MSE % improved relative to classical estimator
Baselines: Classical estimator Prediction mean PPI PT (power-tuned PPI) Shrink-classical Shrink-average UniPT UniPAS
Builds on: Prediction-Powered Inference PPI++ James-Stein estimator Stein's unbiased risk estimate covariate-powered empirical Bayes
Closest papers by meaning
- FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference (ICML 2025 · similarity 0.89)
- Anytime-valid, Bayes-assisted, Prediction-Powered Inference (NeurIPS 2025 · similarity 0.89)
- Regression for the Mean: Auto-Evaluation and Inference with Few Labels through Post-hoc Regression (ICML 2025 · similarity 0.88)
- Prediction-Powered Semi-Supervised Learning with Online Power Tuning (NeurIPS 2025 · similarity 0.86)
- Prediction-Powered E-Values (ICML 2025 · similarity 0.86)
- Stratified Prediction-Powered Inference for Effective Hybrid Evaluation of Language Models (NeurIPS 2024 · similarity 0.85)
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