题目：The Non-Smooth of Quantile Check/Loss Function in Statistics and Deep Learning, Challenges and Solutions

汇报人： 虞克明

会议时间：2025年6月23日(周一)  10：00-11：30

地点： 综合楼644会议室

报告人简介：虞克明，英国伦敦布鲁内尔大学统计与数据科学讲习教授(Chair Professor)、 数学学科研究影响中心主任；英国皇家统计学会会士、英国社科基金 (ESRC) 评审专家成员、英国自科基金 (EPSRC)评审专家成员 、欧洲科学基金(ESF) 评审专家成员。目前是《Journal of the Royal Statistical Society-C》副主编，曾担任过《Journal of the American Statistical Association》、《Journal of the Royal Statistical Society-A》等多家统计权威期刊的副主编。目前他主要从事回归分析、 非参数统计、 机器学习、 贝叶斯推断、大数据及非常小的数据分析等方面的理论和方法研究，是贝叶斯分位数回归方法的开拓者，先后在JASA、JRSSB、JRSSA、JRSSC、JOE、JBES、Bernoulli等统计学顶级刊物上发表论文150多篇。

摘要：Quantiles, which can give some information about the shape of a distribution, are important summary Statistics in data analysis and time series applications. Quantile regression (QR) has applied to wide areas such as environment, medicine, investment, finance, insurance, economics and engineering. In particular, quantile-based check function is listed as an important loss function in Deep Learning. However, lack of smoothness of quantile check/loss function, which means that the first derivative of the function doesn't exist everywhere, has serious consequences on immediate numerical optimisation, more serious in standard errors which may not be well defined from any quantile-based estimation equation and derivation of its asymptotic property (large-sample property). This talk presents some recent research solutions to this challenge.