Extending Prediction-Powered Inference through Conformal Prediction
This work addresses the problem of making black-box ML models more reliable for statistical inference in applications requiring strong guarantees, representing an incremental improvement by building on existing prediction-powered and conformal prediction methods.
The paper tackles the challenge of extending prediction-powered inference to achieve additional guarantees like privacy and robustness, which previously required case-by-case solutions, by integrating it with conformal prediction to ensure validity and handle tasks such as private and time-series data analysis.
Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated conformal set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.