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Schapire and Singer's improved version of AdaBoost for handling weak hypotheses with confidence rated predictions represents an important advance in the theory and practice of boosting. Its success results from a more efficient use of information in weak hypotheses during updating. Instead of simple binary voting a weak hypothesis is allowed to vote for or against a classification with a variable strength or confidence. The Pool Adjacent Violators (PAV) algorithm is a method for converting a score into a probability. We show how PAV may be applied to a weak hypothesis to yield a new weak hypothesis which is in a sense an ideal confidence rated prediction and that this leads to an optimal updating for AdaBoost. The result is a new algorithm which we term PAV-AdaBoost. We give several examples illustrating problems for which this new algorithm provides advantages in performance.

The Synergy Between PAV and AdaBoost