In this paper, we exploit the properties of mean absolute error (MAE) as a loss function for the deep neural network (DNN) based vector-to-vector regression. The goal of this work is two-fold: (i) presenting performance bounds of MAE, and (ii) demonstrating new properties of MAE that make it more appropriate than mean squared error (MSE) as a loss function for DNN based vector-to-vector regression. First, we show that a generalized upper-bound for DNN-based vector- to-vector regression can be ensured by leveraging the known Lipschitz continuity property of MAE. Next, we derive a new generalized upper bound in the presence of additive noise. Finally, in contrast to conventional MSE commonly adopted to approximate Gaussian errors for regression, we show that MAE can be interpreted as an error modeled by Laplacian distribution. Speech enhancement experiments are conducted to corroborate our proposed theorems and validate the performance advantages of MAE over MSE for DNN based regression.

本文探究均方误差作为深度神经网络回归模型的损失函数的性质，提出了均方误差的新特性使其成为更适合于DNN的回归损失函数，并阐述了MAE作为拉普拉斯分布错误的模型的优越性以及实现MAE比MSE更好地拟合深度神经网络回归的性能优势。

基于深度神经网络的向量到向量回归问题的平均绝对误差