Change-point detection for multivariate nonparametric regression with deep neural networks

This article addresses the problem of detecting structural changes in multivariate nonparametric regression models, which commonly arise in high-dimensional and time-dependent data analysis. We propose a CUSUM-type test statistic constructed from estimators obtained via deep neural networks (DNNs). The theoretical properties of the proposed test statistic are rigorously derived under the null and alternative hypotheses. Under the assumptions of a low-dimensional manifold structure in the data support and a hierarchical model architecture, we demonstrate that the DNN-based change-point detection method can effectively mitigate the curse of dimensionality. Furthermore, we establish the asymptotic properties and derive the convergence rate of the estimator for the change-point location. Extensive comparative simulation studies confirm the effectiveness and superior performance of the proposed approach. Finally, we illustrate the practical applicability of the method through an empirical analysis using real-world regional electricity consumption data.