摘要： We study semi-supervised inference for estimating equations using deep neural networks activated by Rectifier Quadratic Unit (ReQU) functions. Building on nonparametric regression with ReQU networks, we effectively integrate information from unlabeled data to construct new semi-supervised estimating equations, and propose a new estimator using one-step update and debiasing strategies. We establish asymptotic normality under mild conditions, demonstrating theoretical optimality of our approach in some sense. To examine those mild conditions, we analyze non-asymptotic error bounds for nonparametric regression and the error bound achieves minimax optimal rate with some lipschitz constraints on the network class. Our framework addresses a general class of estimating equation problems, allowing  the input dimension to be high-dimensional, and the statistical inference does not require any density estimation or bootstrap strategies. We also show that the nonparametric regression using ReQU neural networks can circumvent the curse of dimensionality under the assumptions that the predictor is supported on an approximate low-dimensional manifold and the nonparametric function has a certain inherent structure. 

个人简介：宋珊珊，同济大学数学科学学院助理教授。2020年博士毕业于上海财经大学，随后在香港中文大学统计学系担任博士后研究员，在2024年入职同济大学。她的主要研究兴趣为半监督学习、深度学习理论。2024年入选国家海外青年高层次人才计划，上海市海外青年高层次人才计划，主持国家自然科学青年基金、上海市启明星项目（扬帆专项）。相关成果发表于JASA、JMLR等期刊。