Extension to Infinite Function Classes via Rademacher Complexity

Extend the finite-function-class generalization analysis of the proposed AUC risk estimator for biased positive-unlabeled data with positive-confidence to infinite function classes using Rademacher complexity.

Background

The paper establishes a finite-sample generalization bound for the proposed AUC risk estimator under finite classes of score functions and labeling-probability functions bounded away from zero. The bound accounts for finite-sample error, estimation error in the labeling proportion, confidence error, labeling-probability estimation error, and optimization error.

The authors explicitly restrict this analysis to finite function classes for a self-contained treatment and identify extending it to infinite function classes using Rademacher complexity as future work. Such an extension would provide capacity-sensitive guarantees for more realistic model classes, including neural-network or other nonfinite hypothesis spaces.