A surrogate loss function for optimization of F_β score in binary classification with imbalanced data
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The F_β score is a commonly used measure of classification performance, which plays crucial roles in classification tasks with imbalanced data sets. However, the F_β score cannot be used as a loss function by gradient-based learning algorithms for optimizing neural network parameters due to its non-differentiability. On the other hand, commonly used loss functions such as the binary cross-entropy (BCE) loss are not directly related to performance measures such as the F_β score, so that neural networks optimized by using the loss functions may not yield optimal performance measures. In this study, we investigate a relationship between classification performance measures and loss functions in terms of the gradients with respect to the model parameters. Then, we propose a differentiable surrogate loss function for the optimization of the F_β score. We show that the gradient paths of the proposed surrogate F_β loss function approximate the gradient paths of the large sample limit of the F_β score. Through numerical experiments using ResNets and benchmark image data sets, it is demonstrated that the proposed surrogate F_β loss function is effective for optimizing F_β scores under class imbalances in binary classification tasks compared with other loss functions.
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