PAC-Bayes with Minimax for Confidence-Rated Transduction

We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on these rules, we obtain data-dependent performance guarantees without distributional assumptions on the data. Our analysis techniques are readily extended to a setting in which the predictor is allowed to abstain.