  To have a superior generalization, a deep learning neural network often
involves a large size of training sample. With increase of hidden layers in
order to increase learning ability, neural network has potential degradation in
accuracy. Both could seriously limit applicability of deep learning in some
domains particularly involving predictions of continuous variables with a small
size of samples. Inspired by residual convolutional neural network in computer
vision and recent findings of crucial shortcuts in the brains in neuroscience,
we propose an autoencoder-based residual deep network for robust prediction. In
a nested way, we leverage shortcut connections to implement residual mapping
with a balanced structure for efficient propagation of error signals. The novel
method is demonstrated by multiple datasets, imputation of high spatiotemporal
resolution non-randomness missing values of aerosol optical depth, and
spatiotemporal estimation of fine particulate matter <2.5 \mu m, achieving the
cutting edge of accuracy and efficiency. Our approach is also a general-purpose
regression learner to be applicable in diverse domains.
