A comprehensive theoretical framework for the optimization of neural networks classification performance with respect to weighted metrics
This work addresses a fundamental problem in machine learning for practitioners who need to optimize custom, weighted performance metrics in classification tasks, offering a theoretical foundation that unifies existing methods.
The paper tackles the discrepancy between maximizing weighted classification metrics and minimizing standard loss functions in neural network training by providing a theoretical framework that formalizes weighted metrics and constructs corresponding loss functions. The result is a comprehensive setting that includes established approaches like cost-sensitive learning and weighted cross-entropy as special cases.
In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.