2024/05/14 by Kejin Wu, Wu, Kejin, Dimitris N. Politis +1 · 2 citations
Computer Science · #Anomaly Detection Techniques and Applications #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2405.08276
openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.