  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.
