题目：Multi-Source Sufficient Dimension Reduction via Adaptive Penalization and Subspace Fusion

汇报人：王启华

会议时间：2026年6月4日(周四)      14:00

地点： 综合楼615会议室

报告人简介：

王启华，中国科学院数学与系统科学研究院研究员，博士生导师，国家级高层次人才。曾在北京大学、香港大学任教，先后访问加拿大、美国、德国及澳大利亚10多所世界一流大学。主要从事复杂数据经验似然统计推断、缺失数据分析、高维数据统计分析、大规模数据分析等方面的研究，出版专著三部，在Journal of the Royal Statistical Society Series B (JRSSB), The Annals of Statistics,  Journal of the American Statistical Association (JASA)及Biometrika等国际重要刊物发表论文150余篇,部分工作已产生持久不断的学术影响。曾主持国家杰出青年基金项目、重点项目、多项面上项目，作为核心骨干成员先后参加了两项国家自然科学基金创新群体项目及一项国家重点研发计划项目。

摘要：

With the increasing availability of information from multiple data sources, integrating these data sources effectively has become crucial. However, this task is complicated by the fact that some data sources may be biased due to some reasons such as biased sampling, data corruption, etc.In this paper, the dimension reduction problem is considered in the presence of biased data sources. First, we consider the case where the dimension of the target subspace is known.In this case, two methods, the Robust $L^1$ Loss-based (RL1L) method and the Adaptively Penalized Squared Loss-based (APSL) method, are suggested to estimate the target subspace, by addressing the fact that a data source may still be biased even if its structural dimension equals that of the target subspace.For the case where the dimension of the target subspace is unknown, a major practical challenge arises: we can no longer screen out biased sources based on their structural dimensions directly. Consequently, the dimension and the subspace must be estimated simultaneously.To address this challenge, the APSL method is applied to developing a novel Score and Adaptively Penalized Squared Loss-based (SAPSL) method, which estimates both the dimension and the target subspace simultaneously.It should be highlighted that the first two methods are proposed primarily for the derivation of the third one, although they also have their own practical importance.Some asymptotic properties of the proposed estimators for both the target subspace and dimension are established, and the selection consistency of unbiased data sources is also proved.Simulation studies were conducted to evaluate the proposed estimators, and a real data set was analyzed to illustrate the proposed methods.