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Anytime-valid, Bayes-assisted, Prediction-Powered Inference
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Extends prediction-powered inference to the sequential setting via asymptotic confidence sequences built from KMT strong coupling and the method of mixtures, with Bayes-assisted priors on the prediction rectifier.
Problem
Standard prediction-powered inference (PPI) gives confidence intervals valid only at a fixed labelled sample size, which is inadequate when labelled and unlabelled data arrive over time and conclusions must be drawn continuously.
Approach
Derives anytime-valid PPI confidence sequences by combining asymptotic confidence sequences (almost-sure KMT coupling to i.i.d. Gaussians with Ville's inequality and method of mixtures) with PPI and PPI++ control-variate estimators, and adds a zero-centred prior on the rectifier to tighten intervals when predictions are accurate.
Key results
- On noisy synthetic predictions with sigma_Y=0.1, PPI and PPI++ achieve similar volumes and greatly outperform classical inference, while PPI++ adapts to higher noise levels (sigma_Y=3) where standard PPI loses to classical CS.
- On real mean-estimation datasets (flights, forest, galaxies), PPI methods yield smaller intervals than classical CS with reliable coverage, and Bayes-assisted variants further improve efficiency at moderate labelled sizes.
- Cumulative miscoverage stays below alpha=0.1 for real data experiments, empirically supporting anytime validity.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PPI++ instead of standard PPI as prediction noise increases | PPI confidence sequences · Noisy predictions (σY ∈ {0.1, 0.8, 3}) | average interval volume | Helped |
| Use standard PPI rather than classical inference | confidence sequences · Noisy predictions with small noise | average interval volume | Helped |
| Use standard PPI rather than classical inference | confidence sequences · Noisy predictions with increasing noise | average interval volume | Hurt |
| Add a zero-centred prior on the prediction error (ablation) | PPI confidence sequences · Biased predictions with small bias | average interval volume | Helped |
| Add a zero-centred prior on the prediction error (ablation) | PPI confidence sequences · Biased predictions with large absolute bias | average interval volume | Hurt |
| Use a Gaussian prior rather than Laplace or Student-t (ablation) | Bayes-assisted PPI confidence sequences · Biased predictions | average interval volume | Hurt |
| Use Laplace or Student-t rather than Gaussian prior (ablation) | Bayes-assisted PPI confidence sequences · Biased predictions | average interval volume | Helped |
| Use PPI rather than classical inference | confidence sequences · Flights, Forest, and Galaxies mean estimation | average interval volume | Helped |
| Add Bayes assistance (ablation) | PPI confidence sequences · Flights, Forest, and Galaxies mean estimation | average interval volume | Helped |
| Use PPI rather than classical inference | confidence sequences · Census linear regression and Healthcare logistic regression | average interval volume | Helped |
| Add Bayes assistance (ablation) | PPI confidence sequences · Census linear regression and Healthcare logistic regression | average interval volume | Helped |
| Use PPI rather than classical inference | confidence sequences · Genes quantile estimation | average interval volume | Helped |
Surprising findings
- Bayes-assisted intervals remain valid even under strongly misspecified priors, though they widen when data conflict with the prior.
- For quantile estimation on the genes dataset, Bayes-assisted methods yield larger regions than the other approaches, reflecting lower prediction quality.
Limitations
- Results are asymptotic (almost-sure approximation rates) rather than nonasymptotic, and hold under i.i.d. assumptions plus moment conditions.
- Grid search over theta and numerical integration for non-closed-form priors (e.g., Student-t) add computational cost.
- Experiments assume N = infinity or very large unlabelled pools to isolate the Bayes correction.
Experimental setup
Datasets: flights forest galaxies census healthcare genes
Benchmarks: flights forest galaxies census healthcare genes
Metrics: average interval volume cumulative miscoverage rate
Baselines: classical labelled-only confidence sequence standard PPI PPI++
Builds on: prediction-powered inference PPI++ Bayes-assisted PPI asymptotic confidence sequences KMT strong coupling
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