A new boosting method for a kind of noisy data is developed, where the probability of mislabeling depends on the label of a case. The mechanism of the model is based on a simple idea and gives natural interpretation as a mislabel model. The boosting algorithm is derived from an extension of the exponential loss function, which provides the AdaBoost algorithm. A connection between the proposed method and an asymmetric mislabel model is shown. It is also shown that the loss function proposed constructs a classifier which attains the minimum error rate for a true label. Numerical experiments illustrate how well the proposed method performs in comparison to existing methods.
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