时 间：2024年4月19日 8:30-9:15
地 点：普陀校区理科大楼A1114
报告人：申国豪 香港理工大学助理教授
主持人：於州 华东师范大学教授
摘 要：
We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce the non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating $C^s$ smooth functions with $s >0$ and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests for nonparametric quantile regression.
报告人简介：
申国豪是香港理工大学应用数学系的助理教授。2022年毕业于香港中文大学获统计学博士学位。他的研究兴趣包括统计机器学习和非参数统计学，尤其关注深度学习的基础理论。他的研究成果已发表在Annals of Statistics, Biometrika, Journal of Machine Learning Research, Journal of Econometrics, and NeurIPS 等期刊和会议上。