  Deep neural networks (DNN) has received increasing attention in machine
learning applications in the last several years. Recently, a non-asymptotic
error bound has been developed to measure the performance of the fully
connected DNN estimator with ReLU activation functions for estimating
regression models. The paper at hand gives a small improvement on the current
error bound based on the latest results on the approximation ability of DNN.
More importantly, however, a non-random subsampling technique--scalable
subsampling--is applied to construct a `subagged' DNN estimator. Under
regularity conditions, it is shown that the subagged DNN estimator is
computationally efficient without sacrificing accuracy for either estimation or
prediction tasks. Beyond point estimation/prediction, we propose different
approaches to build confidence and prediction intervals based on the subagged
DNN estimator. In addition to being asymptotically valid, the proposed
confidence/prediction intervals appear to work well in finite samples. All in
all, the scalable subsampling DNN estimator offers the complete package in
terms of statistical inference, i.e., (a) computational efficiency; (b) point
estimation/prediction accuracy; and (c) allowing for the construction of
practically useful confidence and prediction intervals.
