用最小误差熵原则训练深度网络，实现强混合数据下的最优回归性能。
Deep regression learning from dependent observations with minimum error entropy principle
- 基于最小误差熵的深度神经网络，处理强混合观测数据。
- 在高斯误差下达到极小最大风险上界，逼近理论最优收敛率。
- 适合需要高鲁棒性非参数回归的研究者，尤其关注数据相关性场景。
本文研究从强混合观测中进行非参数回归的问题。提出的方法基于深度神经网络与最小误差熵（MEE）原则，考察两种估计器：非正则化深度神经网络（NPDNN）和稀疏正则化深度神经网络（SPDNN）。针对Hölder类和复合Hölder函数类，建立了两种估计器的期望超额风险上界。对于高斯误差模型，所得上界逼近（对数因子内）文献\cite{schmidt2020nonparametric}建立的下界，表明基于MEE的NPDNN与SPDNN在强混合数据下可实现极小最大风险意义下的最优收敛率。
原文摘要 · Abstract (English)
This paper considers nonparametric regression from strongly mixing observations. The proposed approach is based on deep neural networks with minimum error entropy (MEE) principle. We study two estimators: the non-penalized deep neural network (NPDNN) and the sparse-penalized deep neural network (SPDNN) predictors. Upper bounds of the expected excess risk are established for both estimators over the classes of Hölder and composition Hölder functions. For the models with Gaussian error, the rates of the upper bound obtained match (up to a logarithmic factor) with the lower bounds established in \cite{schmidt2020nonparametric}, showing that both the MEE-based NPDNN and SPDNN estimators from strongly mixing data can achieve the minimax optimal convergence rate.
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