A surrogate loss function for optimization of $F_β$ score in binary classification with imbalanced data
This addresses a bottleneck in gradient-based learning for imbalanced classification tasks, offering a practical improvement for researchers and practitioners in machine learning.
The paper tackles the problem of optimizing the non-differentiable F_β score in binary classification with imbalanced data by proposing a differentiable surrogate loss function, demonstrating its effectiveness in improving F_β scores compared to other loss functions through numerical experiments on benchmark image datasets.
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.