In this paper, we show that, in vector-to-vector regression utilizing deep neural networks (DNNs), a generalized loss of mean absolute error (MAE) between the predicted and expected feature vectors is upper bounded by the sum of an approximation error, an estimation error, and an optimization error. Leveraging upon error decomposition techniques in statistical learning theory and non-convex optimization theory, we derive upper bounds for each of the three aforementioned errors and impose necessary constraints on DNN models. Moreover, we assess our theoretical results through a set of image de-noising and speech enhancement experiments. Our proposed upper bounds of MAE for DNN based vector-to-vector regression are corroborated by the experimental results and the upper bounds are valid with and without the “over-parametrization” technique.

中文翻译：

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分析基于深度神经网络的向量到向量回归的平均绝对误差的上限

在本文中，我们表明，在利用深度神经网络 (DNN) 的向量到向量回归中，预测和预期特征向量之间的平均绝对误差 (MAE) 的广义损失上限为近似误差之和，估计误差和优化误差。利用统计学习理论和非凸优化理论中的误差分解技术，我们推导出上述三个误差中的每一个的上限，并对 DNN 模型施加必要的约束。此外，我们通过一组图像去噪和语音增强实验来评估我们的理论结果。我们提出的基于 DNN 的向量到向量回归的 MAE 上限得到了实验结果的证实，无论是否使用“过度参数化”技术，上限都是有效的。