Pro-active inference improves accuracy in costly data sampling
Pro-Active Inference
Machine Learning
Summary
Measuring the average outcome in a population is important but often expensive because you can't collect every data point. The authors introduce a method called Pro-Active Inference (PAI) that smartly picks which data points to label next by using existing predictions and information from the whole group. This approach updates predictions on the fly as new labels come in and aims to give precise estimates without wasting resources. Tests on multiple datasets show it usually outperforms previous methods, revealing when its adaptability helps or sometimes even hinders accuracy.
What this means in practice
- •For clinical trial managers: Select patient outcomes to observe cost-effectively while updating risk predictions throughout the trial.
- •For marketing analytics teams: Improve survey data collection by choosing which customers to sample next to better estimate average preferences.
Authors
Skyler Wu, Yash Nair, Antoine Maechler, Emmanuel J. Candès
Abstract
Estimating a population mean is fundamental across scientific applications, but observing every outcome can be prohibitively expensive. Often, covariates and machine learning (ML) predictions are available for the full population, even when only a small subset of outcomes can be observed. How can we leverage this information to proactively select observations to label, update ML predictions as labels arrive, and construct statistically valid confidence intervals? We develop a general, without-replacement formulation of Pro-Active Inference (PAI), extending our earlier with-replacement approach and building on Active Statistical Inference. Rather than making fixed-order label-skip decisions, PAI proactively selects which observation to label next from the remaining covariate pool while accommodating online ML updates. We establish PAI's finite-sample unbiasedness and asymptotic validity, develop an improved finite-sample variance estimator, and extend PAI to superpopulation inference without Bonferroni corrections or $α$-splitting. We characterize PAI's potential efficiency gains over Batch Active Inference in a quasi-oracle setting, highlighting the role of prediction-residual imbalance. Across eight diverse datasets, PAI achieves greater sampling efficiency than Sequential Active Inference in the vast majority of tested settings with near-nominal statistical coverage, using the same ML predictor and uncertainty score. However, comparisons with simpler baselines such as Prediction-Powered Inference and uniform sampling, as well as the closely related Prediction-Powered Active Testing, reveal when additional adaptivity helps or hurts statistical efficiency. Through interpretable, theory-motivated diagnostics and frozen-ML ablations, we investigate when and why PAI gains or loses efficiency, highlighting the initial residual-estimation problem and subsequent online learning dynamics.