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Upper Bounds for Error Rates Associated to Linear Combinations of Classifiers

A practical and useful notion of weak dependence between many classifiers constructed with the same training data is introduced. It is shown that when (a) this weak dependence is rather low, and (b) the expected margins are large, exponential bounds on the true error rates can be achieved. Empirical results with randomized trees, and trees constructed via boosting and adaptive bagging, show that, to some extent, weak dependence is present in these type of trees.