Prediction-Powered E-Values

2025-02-06

AI Summary

This work addresses the unreliability of statistical inference under small-sample or data-scarce regimes. We propose a prediction-driven e-value inference framework that systematically extends predictive modeling to the general e-value paradigm—beyond prior Z-estimator–specific approaches (e.g., for means or quantiles). Our method integrates predictive models (e.g., regressors or classifiers) with e-value theory via a modular, plug-and-play architecture, inherently preserving anytime-validity, posterior validity, and sequential scalability. It supports arbitrary e-value–expressible tasks, including hypothesis testing, confidence set construction, changepoint detection, and causal discovery. Experiments demonstrate that our framework substantially surpasses the limitations of Z-estimation across diverse inference tasks, significantly improving robustness and practical utility in low-data settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to Z-estimation problems such as inference of means and quantiles. In this paper, we apply ideas of prediction-powered inference to e-values. By doing so, we inherit all the usual benefits of e-values -- such as anytime-validity, post-hoc validity and versatile sequential inference -- as well as greatly expand the set of inferences achievable in a prediction-powered manner. In particular, we show that every inference procedure that can be framed in terms of e-values has a prediction-powered counterpart, given by our method. We showcase the effectiveness of our framework across a wide range of inference tasks, from simple hypothesis testing and confidence intervals to more involved procedures for change-point detection and causal discovery, which were out of reach of previous techniques. Our approach is modular and easily integrable into existing algorithms, making it a compelling choice for practical applications.

Problem

• Extends prediction-powered inference to e-values
• Enables wider range of inference tasks
• Integrates modularly into existing algorithms

Innovation

• Prediction-powered e-values expansion
• Modular integration into algorithms
• Versatile sequential inference enhancement