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On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regression

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Document pages: 5 pages

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

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