  While reliable data-driven decision-making hinges on high-quality labeled
data, the acquisition of quality labels often involves laborious human
annotations or slow and expensive scientific measurements. Machine learning is
becoming an appealing alternative as sophisticated predictive techniques are
being used to quickly and cheaply produce large amounts of predicted labels;
e.g., predicted protein structures are used to supplement experimentally
derived structures, predictions of socioeconomic indicators from satellite
imagery are used to supplement accurate survey data, and so on. Since
predictions are imperfect and potentially biased, this practice brings into
question the validity of downstream inferences. We introduce cross-prediction:
a method for valid inference powered by machine learning. With a small labeled
dataset and a large unlabeled dataset, cross-prediction imputes the missing
labels via machine learning and applies a form of debiasing to remedy the
prediction inaccuracies. The resulting inferences achieve the desired error
probability and are more powerful than those that only leverage the labeled
data. Closely related is the recent proposal of prediction-powered inference,
which assumes that a good pre-trained model is already available. We show that
cross-prediction is consistently more powerful than an adaptation of
prediction-powered inference in which a fraction of the labeled data is split
off and used to train the model. Finally, we observe that cross-prediction
gives more stable conclusions than its competitors; its confidence intervals
typically have significantly lower variability.
