【报告题目】Model-free variable importance testing with machine learning methods
【时 间】2024年12月5日（周四） 14:00-15:00
【地 点】主楼D601
【报 告人】郭旭 教授（北京师范大学）
【报告人简介】 郭旭博士，现为北京师范大学统计学院教授，博士生导师。郭老师一直从事回归分析中复杂假设检验的理论方法及应用研究，近年来旨在对高维数据发展适当有效的检验方法。部分成果发表在JRSSB, JASA，Biometrika，JOE和NeurIPS。现主持国家自然科学基金优秀青年基金。曾荣获北师大第十一届“最受本科生欢迎的十佳教师”，北师大第十八届青教赛一等奖和北京市第十三届青教赛三等奖。
【报告内容简介】 In this talk, we investigate variable importance testing problem in a model-free framework. Some remarkable procedures are developed recently. Despite their success, existing procedures suffer from a significant limitation, that is, they generally require larger training sample and do not have the fastest possible convergence rate under alternative hypothesis. In this paper, we propose a new procedure to test variable importance. Flexible machine learning methods are adopted to estimate unknown functions. Under null hypothesis, our proposed test statistic converges to standard chi-squared distribution. While under local alternative hypotheses, it converges to non-central chi-square distribution. It has non-trivial power against the local alternative hypothesis which converges to the null at the fastest possible rate. We also extend our procedure to test conditional independence. Asymptotic properties are also developed. Numerical studies and two real data examples are conducted to illustrate the performance of our proposed test statistic.
数理学院
2024年12月3日
