Prediction-Powered E-Values

TL;DR

This paper introduces a novel prediction-powered inference framework using e-values, enabling versatile, anytime-valid, and post-hoc valid inferences across various statistical tasks, including hypothesis testing, change-point detection, and causal discovery.

Contribution

It extends prediction-powered inference to e-values, broadening the scope of inference procedures that can be performed in a prediction-powered manner.

Findings

Effective across multiple inference tasks

Supports anytime-valid and post-hoc inference

Integrates easily with existing algorithms

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.