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Task-Agnostic Machine-Learning-Assisted Inference
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Proposes PSPS, a task-agnostic post-prediction inference protocol that runs existing analysis routines on labeled and unlabeled ML-predicted data, then combines their summary statistics via one-step debiasing to get valid, efficient inference.
Problem
Post-prediction statistical inference with ML-predicted outcomes is limited to a few M-estimation tasks (mean, quantile, linear, logistic regression) because each new task needs bespoke derivations and software, so valid ML-assisted inference cannot be applied to most existing statistical tools.
Approach
Apply the existing analysis routine to labeled data (observed outcome), labeled data (predicted outcome), and unlabeled data (predicted outcome), plus bootstrap covariance, and combine the resulting summary statistics with an optimal one-step debiasing weight; this works for any estimator that is asymptotically normal, needs only summary statistics, and is robust to arbitrary ML models.
Key results
- In simulations, PSPS gives correct coverage with narrower confidence intervals than classical and other ML-assisted methods for mean, linear and logistic regression, and extends to quantile, IV, NB regression, debiased Lasso and Wilcoxon rank-sum tests where the imputation-based method fails.
- PSPS-BH and PSPS-knockoff control FDR while achieving higher power than classical labeled-only methods; imputation-based methods fail to control FDR.
- On UK Biobank DXA-BMD vQTL analysis, PSPS identified 108 significant variants (FDR < 0.05) across 5 independent loci, whereas the classical labeled-only method found none.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PSPS instead of classical inference using labeled data only | ML-assisted quantile regression for DXA-BMD vQTL discovery · UK Biobank DXA-BMD | significant variants at FDR < 0.05: No genetic variants reached statistical significance -> 108 significant variants | Helped |
| Use PSPS rather than classical inference using labeled data only | Mean estimation, linear regression, and logistic regression with ML predictions · Simulations with implemented tasks | confidence interval width | Helped |
| Use imputation-based inference on unlabeled data only | Mean estimation, linear regression, and logistic regression with ML predictions · Simulations with implemented tasks | confidence interval coverage | Hurt |
| Use PSPS rather than classical inference using labeled data only | Quantile regression, IV regression, NB regression, and debiased Lasso · Simulations with tasks not implemented for existing ML-assisted inference | confidence interval width | Helped |
| Use PSPS rather than classical inference using labeled data only | Wilcoxon rank-sum test · Simulations with tasks not implemented for existing ML-assisted inference | statistical power | Helped |
| Use imputation-based inference on unlabeled data only | Quantile regression, IV regression, NB regression, and debiased Lasso · Simulations with tasks not implemented for existing ML-assisted inference | confidence interval coverage | Hurt |
| Use imputation-based inference on unlabeled data only | Wilcoxon rank-sum test · Simulations with tasks not implemented for existing ML-assisted inference | type-I error | Hurt |
| Increase unlabeled sample size | PSPS · Simulated parameter-estimation tasks | confidence interval width | Helped |
| Use PSPS-BH or PSPS-knockoff rather than classical FDR control | ML-assisted feature selection · Low-dimensional and high-dimensional linear regression simulations | statistical power | Helped |
| Use imputation-based FDR control | Feature selection · Low-dimensional and high-dimensional linear regression simulations | FDR control | Hurt |
| Use a matrix-valued weight rather than the scalar weight used by PPI++ | PSPS versus PPI++ · M-estimation problems | asymptotic variance | Helped |
| Add unlabeled-data ML predictions with the PSPS debiasing step | Classical estimator based on labeled data · General estimation under the stated assumptions | asymptotic variance | Helped |
Surprising findings
- The imputation-based method fails to achieve valid coverage and shows inflated type-I error even though ML predictions are used, illustrating the need for debiasing.
Limitations
- Relies on bootstrap resampling, which is computationally heavier than closed-form ML-assisted methods.
- Requires labeled and unlabeled data to be i.i.d. (distributional shift needs sensitivity analysis).
Experimental setup
Datasets: simulated data UK Biobank
Benchmarks: simulations (mean, linear, logistic, quantile, IV, negative binomial, debiased Lasso, Wilcoxon rank-sum, FDR control) UK Biobank DXA-BMD vQTL analysis
Metrics: confidence interval coverage confidence interval width type-I error statistical power FDR runtime
Baselines: classical labeled-only inference imputation-based inference PPI PPI++ PSPA
Builds on: PPI (prediction-powered inference) PPI++ PSPA knockoff debiased Lasso
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