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Title: Adaptive deep learning for nonparametric time series regression Authors:  Daisuke Kurisu - The University of Tokyo (Japan) [presenting]
Riku Fukami - (Japan)
Yuta Koike - University of Tokyo (Japan)
Abstract: A general theory is developed for adaptive nonparametric estimation of mean functions of nonstationary and nonlinear time series using deep neural networks (DNNs). We first consider two types of DNN estimators, non-penalized and sparse-penalized DNN estimators, and establish their generalization error bounds for general nonstationary time series. We then derive minimax lower bounds for estimating mean functions belonging to a wide class of nonlinear autoregressive (AR) models that include nonlinear generalized additive AR, single index, and threshold AR models. Building upon the results, we show that the sparse-penalized DNN estimator is adaptive and attains the minimax optimal rates up to a poly-logarithmic factor for many nonlinear AR models. Through numerical simulations, we demonstrate the usefulness of the DNN methods for estimating nonlinear AR models with intrinsic low-dimensional structures and discontinuous or rough mean functions, which is consistent with our theory.