Not All Teachers Are Created Equal: Confidence-Aware Prediction-Powered Learning from Heterogeneous Teachers

Semi-supervised learning often uses teacher predictions to exploit unlabeled data, but unreliable predictions can introduce harmful supervision. This problem is especially acute when teachers are reliable only on particular inputs, classes, or domains. Prediction-powered inference (PPI) is a general statistical framework that combines predictions with labeled-data corrections to construct unbiased estimators. Building on this principle, we introduce confidence-aware prediction-powered correction (C-PP), which adapts to instance-dependent teacher reliability, and covariance-aware multi-teacher correction (CM-PP), which combines complementary teachers while accounting for their dependence. We establish finite-sample variance bounds and convergence guarantees, and develop online weight updates that avoid explicit variance estimation. Across image and tabular classification, and semantic segmentation, C-PP and CM-PP improve upon confidence-agnostic prediction-powered learning and established semi-supervised baselines under teacher-reliability shifts, partial coverage, and heterogeneous specialization.