Although increasing hidden layers can improve the ability of a neural network in modeling complex nonlinear relationships, deep layers may result in degradation of accuracy due to the problem of vanishing gradient. Accuracy degradation limits the applications of deep neural networks to predict continuous variables with a small sample size and/or weak or little invariance to translations. Inspired by residual convolutional neural network in computer vision, we developed an encoder–decoder full residual deep network to robustly regress and predict complex spatiotemporal variables. We embedded full shortcuts from each encoding layer to its corresponding decoding layer in a systematic encoder–decoder architecture for efficient residual mapping and error signal propagation. We demonstrated, theoretically and experimentally, that the proposed network structure with full residual connections can successfully boost the backpropagation of signals and improve learning outcomes. This novel method has been extensively evaluated and compared with four commonly used methods (i.e., plain neural network, cascaded residual autoencoder, generalized additive model, and XGBoost) across different testing cases for continuous variable predictions. For model evaluation, we focused on spatiotemporal imputation of satellite aerosol optical depth with massive nonrandomness missingness and spatiotemporal estimation of atmospheric fine particulate matter $\leq 2.5~\mu \text{m}$ (PM _2.5 ). Compared with the other approaches, our method achieved the state-of-the-art accuracy, had less bias in predicting extreme values, and generated more realistic spatial surfaces. This encoder–decoder full residual deep network can be an efficient and powerful tool in a variety of applications that involve complex nonlinear relationships of continuous variables, varying sample sizes, and spatiotemporal data with weak or little invariance to translation.

中文翻译：

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用于鲁棒回归和时空估计的编码器-解码器全残差深度网络

虽然增加隐藏层可以提高神经网络建模复杂非线性关系的能力，但深层可能会因梯度消失问题而导致精度下降。精度下降限制了深度神经网络在预测小样本和/或平移不变性弱或很小的连续变量方面的应用。受计算机视觉中残差卷积神经网络的启发，我们开发了一种编码器-解码器全残差深度网络，以稳健地回归和预测复杂的时空变量。我们在系统编码器-解码器架构中嵌入了从每个编码层到其相应解码层的完整快捷方式，以实现有效的残差映射和误差信号传播。我们从理论上和实验上证明，所提出的具有完整残差连接的网络结构可以成功地促进信号的反向传播并改善学习成果。这种新颖的方法已经在连续变量预测的不同测试案例中与四种常用方法（即普通神经网络、级联残差自动编码器、广义加性模型和 XGBoost）进行了广泛的评估和比较。对于模型评估，我们重点关注具有大量非随机缺失的卫星气溶胶光学深度的时空插补以及大气细颗粒物的时空估计 $\leq 2.5~\mu \text{m}$（下午 _2.5 ）。与其他方法相比，我们的方法实现了最先进的精度，预测极值的偏差较小，并生成了更真实的空间表面。这种编码器-解码器全残差深度网络可以成为各种应用中高效且强大的工具，这些应用涉及连续变量的复杂非线性关系、不同的样本大小以及平移不变性弱或很小的时空数据。