报告题目：A unified generalization of inverse regression via adaptive column selection

报告时间：2023年3月29日 上午 10:00

会议链接：https://meeting.tencent.com/dm/fjVehSBwoaqn

会议 ID：677-312-219

主办单位：科研处/数学与统计学院

主讲人：骆威

骆威简介：骆威于2014年毕业于美国宾夕法尼亚州立大学，之后任职于美国Baruch College,于2018年加入浙江大学。骆威的研究方向包括充分降维和因果推断，在Annals of Statistics, Biometrika, JRSSB等统计国际学术期刊上发表了多篇论文。

摘要：Higher-order inverse regression methods are commonly known as more powerful sufficient dimension reduction (SDR) methods than the popularly used sliced inverse regression (SIR) in the population level. However, due to the convention of essentially conducting singular value decomposition on the ambient candidate matrices, these methods suffer from the excessive number of parameters in the sample level and have not been systematically generalized under the high-dimensional settings like SIR. In this paper, we break the convention of using the ambient candidate matrices in these methods, and instead apply a novel column-selection strategy on their candidate matrices that substantially lowers down the working number of parameters to being comparable with SIR. Then, for the first time of the literature, we generalize the higher-order inverse regression methods, as well as their ensembles, towards sparsity under the high-dimensional settings in a uniform manner. The dimension of the predictor is allowed to diverge with the sample size in nearly an exponential order, and no additional restrictions are imposed on the data other than those commonly seen in the high-dimensional literature. For completeness of theory, we also study the column-selection strategy towards the estimation efficiency under the conventional low-dimensional settings. These results are illustrated by simulation studies and a real data application at the end.