报告题目：Multi-task Dimension Reduction via Common Ambient Space
报告人：王启华 (中国科学院数学与系统科学研究院)
讲座时间：2026年10月15号14:30-15:30
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，国家杰出青年基金获得者，教育部高层次特聘教授，中科院核心骨干研究员。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。
报告摘要：
Multi-task learning often assumes a shared subspace across all tasks, a condition that fails when their intersection is empty. We break this restrictive ``common core'' paradigm and propose a flexible Approximate Common Ambient Space (ACAS) framework, where only a subset of task subspaces need lie near a low-dimensional ambient space, while others are allowed to deviate. The main challenges are the unknown set of conforming tasks and the risk of negative transfer from non-conforming ones. To address these, we develop ACAS based dimension reduction (ACAS-DR) method: a penalized optimization approach that jointly estimates the ambient space and individual subspaces, and its enhanced version CAS-DR for exact containment. Theoretically, we establish non-asymptotic error bounds showing that both estimators improve over single-task methods without inflating errors for non-conforming tasks. When the conforming task subspaces are exactly contained in the ambient space, CAS-DR further improves upon ACAS-DR with sharper error bounds. Simulations demonstrate substantial gains over local estimation and naive pooling. An analysis of Beijing air-quality data illustrates the proposed methods. Our framework shifts from seeking a common intersection to a common container, greatly expanding applicability while retaining robustness.Critically, it offers a principled and practical solution for multi-task dimension reduction with heterogeneous task structures---a setting that existing shared-subspace methods cannot accommodate.
