Multiclass neural network classifiers are typically trained using
cross-entropy loss. Following training, the performance of this same neural
network is evaluated using an application-specific metric based on the
multiclass confusion matrix, such as the Macro $F_\beta$-Score. It is
questionable whether the use of cross-entropy will yield a classifier that
aligns with the intended application-specific performance criteria,
particularly in scenarios where there is a need to emphasize one aspect of
classifier performance. For example, if greater precision is preferred over
recall, the $\beta$ value in the $F_\beta$ evaluation metric can be adjusted
accordingly, but the cross-entropy objective remains unaware of this preference
during training. We propose a method that addresses this training-evaluation
gap for multiclass neural network classifiers such that users can train these
models informed by the desired final $F_\beta$-Score. Following prior work in
binary classification, we utilize the concepts of the soft-set confusion
matrices and a piecewise-linear approximation of the Heaviside step function.
Our method extends the $2 \times 2$ binary soft-set confusion matrix to a
multiclass $d \times d$ confusion matrix and proposes dynamic adaptation of the
threshold value $\tau$, which parameterizes the piecewise-linear Heaviside
approximation during run-time. We present a theoretical analysis that shows
that our method can be used to optimize for a soft-set based approximation of
Macro-$F_\beta$ that is a consistent estimator of Macro-$F_\beta$, and our
extensive experiments show the practical effectiveness of our approach.

我们提出了一种方法，该方法可以为多类神经网络分类器提供训练和评估的一致性，使其与预期的特定应用性能标准相一致，并通过使用软集混淆矩阵和分段线性逼近的概念，将二元情况扩展到多类情况。