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浙江大学骆威副教授:On efficient dimension reduction with respect to the interaction between two response variables

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主 题On efficient dimension reduction with respect to the interaction between two response variables

主讲人浙江大学骆威副教授

主持人统计学院林华珍教授

时间:2023年3月31日(周五)下午14:00-15:00

举办地点:柳林校区弘远楼408会议室

主办单位:统计研究中心和统计学院 科研处

主讲人简介:

骆威,浙江大学副教授。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。他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,目前主持国家优秀青年科学基金项目。


内容简介

In this paper, we propose the theory and the methodologies for dimension reduction with respect to the interaction between two response variables. This is crucial for effective dimension reduction in applications such as missing data analysis and causal inference. We introduce the concepts of the locally and the globally efficient dimension reduction subspaces, which induce reduced predictors that preserve the key feature for subsequent data analysis. These spaces can be low dimensional when neither of the two individual response variables are equipped with low-dimensional data structures, for which they cannot be recovered by the existing dimension reduction applications in general. Based on the existing inverse regression methods, we propose a family of dimension reduction methods called the dual inverse regression, which consistently estimate the locally efficient dimension reduction subspaces under mild assumptions and consistently estimate the globally efficient dimension reduction subspace when it exists. These methods are also easily implementable. In addition, we propose a sufficient and necessary condition for the existence of the globally efficient dimension reduction subspace that is handy to check. We illustrate the usefulness of the proposed dual inverse regression methods by simulations studies and a real data example at the end.

在本文中,主讲人提出了关于两个响应变量之间相互作用的降维理论和方法。这对于缺失数据分析和因果推断等应用中的有效降维至关重要。主讲人引入了局部和全局有效降维子空间的概念,这些子空间诱导了为后续数据分析保留关键特征的约简预测因子。当两个单独的响应变量都没有配备低维数据结构时,这些空间可能是低维的,通常现有的降维应用程序无法恢复低维数据结构。基于现有的逆回归方法,主讲人提出了一种称为对偶逆回归的降维方法,该方法在温和假设下一致估计局部有效降维子空间,在存在全局有效降维子空间时一致估计全局有效降维子空间。这些方法也很容易实现。此外,主讲人还提出了易于检验的全局有效降维子空间存在的充要条件。最后通过仿真研究和一个实际数据实例说明了所提出的对偶逆回归方法的有效性。




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