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Optimal Binary Classifier Aggregation for General Losses

Akshay Balsubramani · Yoav S Freund

Area 5+6+7+8 #148

Keywords: [ Ensemble Methods and Boosting ] [ Game Theory and Econometrics ] [ Learning Theory ]


We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions for a very general class of loss functions including all convex and many non-convex losses, extending a recent analysis of the problem for misclassification error. The result is a family of semi-supervised ensemble aggregation algorithms which are as efficient as linear learning by convex optimization, but are minimax optimal without any relaxations. Their decision rules take a form familiar in decision theory -- applying sigmoid functions to a notion of ensemble margin -- without the assumptions typically made in margin-based learning.

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