  We present PPI++: a computationally lightweight methodology for estimation
and inference based on a small labeled dataset and a typically much larger
dataset of machine-learning predictions. The methods automatically adapt to the
quality of available predictions, yielding easy-to-compute confidence sets --
for parameters of any dimensionality -- that always improve on classical
intervals using only the labeled data. PPI++ builds on prediction-powered
inference (PPI), which targets the same problem setting, improving its
computational and statistical efficiency. Real and synthetic experiments
demonstrate the benefits of the proposed adaptations.
