论文标题
分析基于深神经网络的矢量回归的平均绝对误差的上限
Analyzing Upper Bounds on Mean Absolute Errors for Deep Neural Network Based Vector-to-Vector Regression
论文作者
论文摘要
在本文中，我们表明，在使用深神经网络（DNNS）的向量到矢量回归中，预测特征向量和预期特征向量之间的平均绝对误差（MAE）的普遍丢失是由近似误差的总和，估计误差和优化误差的上限。利用统计学习理论和非凸优化理论中的误差分解技术，我们为上述三个错误中的每一个都得出了上限，并对DNN模型施加了必要的约束。此外，我们通过一系列图像去噪声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MAE的上限基于DNN的载体到向量回归是通过实验结果确认的，并且上限对有效，也没有“过度参数化”技术。
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.
