An End-to-End Approach for Training Neural Network Binary Classifiers on Metrics Based on the Confusion Matrix

While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-testing gap be addressed? While specific techniques have been adopted to optimize certain confusion matrix based metrics, it is challenging or impossible in some cases to generalize the techniques to other metrics. Adversarial learning approaches have also been proposed to optimize networks via confusion matrix based metrics, but they tend to be much slower than common training methods. In this work, we propose to approximate the Heaviside step function, typically used to compute confusion matrix based metrics, to render these metrics amenable to gradient descent. Our extensive experiments show the effectiveness of our end-to-end approach for binary classification in several domains.