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In recent years, imbalanced learning problem has attracted more and more attentions from both academia and industry, and the problem is concerned with the performance of learning algorithms in the presence of data with severe class distribution skews. In this paper, we apply the well-known statistical model logistic discrimination to this problem and propose a novel method to improve its performance. To fully consider the class imbalance, we design a new cost function which takes into account the accuracies of both positive class and negative class as well as the precision of positive class. Unlike traditional logistic discrimination, the proposed method learns its parameters by maximizing the proposed cost function. Experimental results show that, compared with other state-of-the-art methods, the proposed one shows significantly better performance on measures of recall, g-mean, f-measure, AUC, and accuracy. [ABSTRACT FROM AUTHOR]