摘要：We will provide a brief summary of some results appeared in kernel regression/deep neural network and propose some potential directions.

简介：魏哲巍，中国人民大学高瓴人工智能学院教授，博导，入选国家高层次青年人才。2008年本科毕业于北京大学数学科学学院，2012年博士毕业于香港科技大学计算机系；2012年至2014年于奥胡斯大学海量数据算法研究中心担任博士后研究员，2014年9月加入中国人民大学担任副教授，2019年8月起任教授。数据库、理论计算机、数据挖掘、机器学习等领域的顶级会议及期刊上（如SIGMOD、VLDB、ICML、NeurIPS、KDD、SODA等）发表论文60余篇，并获得数据库理论顶级会议PODS2022时间检验奖。主持自然科学基金重点项目、科技部2030重点专项课题。担任PODS、ICDT等大数据理论会议论文集主席以及ICML、NeurIPS、WWW领域主席；担任鹏城实验室广州基地青年科学家。培养博士生获2021年百度奖学金（全球10人）、2022年微软学者（亚太地区12人）。

摘要：This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.