Post-hoc calibration of miscalibrated black-box predictions on a labeled sample improves efficiency of prediction-powered inference for semisupervised mean estimation.
Expanding the variance ofu⊤Dm(O)therefore yields Var[u⊤Dm(O)] = Var[u⊤Deff(O)] +E P0 1−π 0(X) π0(X) u⊤A−1 0 δm(X) 2
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Calibeating Prediction-Powered Inference
Post-hoc calibration of miscalibrated black-box predictions on a labeled sample improves efficiency of prediction-powered inference for semisupervised mean estimation.