Prediction-Powered E-Values

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.

Quality statistical inference requires data, which can be missing or hard to obtain. It is tempting to resolve this by using predictions from powerful ML models to fill this missing data, but this can lead to biased inferences due to the model's imperfections. A recent line of work, termed 'prediction-powered inference,' seeks to design procedures to debias such inferences.In our paper, we extend prediction-powered inference to work with e-values, a modern enticing alternative to p-values. Besides inheriting the various favorable properties of e-values over p-values, doing so significantly expands the set of inferences that can be done in a prediction-powered manner; this was previously restricted to problems that fit into a 'Z-estimation' framework, which includes means, quantiles and linear regression coefficients, but not much more. With our method, on the other hand, any inference task that can be done with e-values (which is a very large class) can be done in a prediction-powered setting.We showcase the effectiveness of our method 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.