# Active Multiple-Prediction-Powered Inference

arXiv: https://arxiv.org/abs/2605.08429 · HTML: https://mlsanity.com/paper/2605.08429/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Stratified Prediction-Powered Inference for Hybrid Language Model Evaluation](https://mlsanity.com/paper/2406.04291/) (2024)
- [Reliable and Trustworthy Machine Learning for Health Using Dataset Shift Detection](https://mlsanity.com/paper/2110.14019/) (2021)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [VeriFact: Verifying Facts in LLM-Generated Clinical Text with Electronic Health Records](https://mlsanity.com/paper/2501.16672/) (2025)
- [Task-Agnostic Machine-Learning-Assisted Inference](https://mlsanity.com/paper/2405.20039/) (2024)
- [Sequential Harmful Shift Detection Without Labels](https://mlsanity.com/paper/2412.12910/) (2024)
- [Statistically Valid Post-Deployment Monitoring Should Be Standard for AI-Based Digital Health](https://mlsanity.com/paper/2506.05701/) (2025)
- [Anytime-valid, Bayes-assisted, Prediction-Powered Inference](https://mlsanity.com/paper/2505.18000/) (2025)
- [Robust Sampling for Active Statistical Inference](https://mlsanity.com/paper/2511.08991/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Surrogate Is Not the Reward: Post-Surrogate Primary-Outcome Acquisition in Contextual Bandits](https://mlsanity.com/paper/2610.06610/) (2026)

## Abstract (arXiv)

Post-deployment monitoring of healthcare AI requires statistically valid, label-efficient methods, but gold-standard labels from clinician chart review are expensive. Prediction-powered inference (PPI) and active statistical inference (ASI) reduce label cost by combining a small labeled sample with abundant model predictions, but both are restricted to a single predictor, a poor fit for modern clinical pipelines that have multiple predictors of differing cost and accuracy available at inference time. We propose Active Multiple-Prediction-Powered Inference (AM-PPI), which routes each instance to a cost-appropriate predictor subset, samples gold-standard labels in proportion to the chosen subset's residual uncertainty, and reweights predictions to minimize estimator variance, all under a single deployment-time budget. AM-PPI generalizes ASI to leverage multiple predictors and extends Multiple-PPI from global per-predictor allocation to per-instance adaptive routing. We derive closed-form Karush-Kuhn-Tucker (KKT) conditions for all three decisions and prove, via biconvexity and strong duality, that the resulting fixed point is a global optimum despite the joint problem being non-jointly-convex. We establish asymptotic normality with valid coverage, minimum-variance unbiasedness within the linear-prediction augmented inverse propensity weighted (AIPW) class, and a closed-form criterion identifying when multiple predictors help. On synthetic data and three healthcare monitoring tasks, AM-PPI produces 10 to 40 percent narrower confidence intervals (CIs) than single-predictor ASI in the budget regime where routing matters, and matches the better baseline elsewhere.