时 间：2026年3月20日（周五） 10：30 – 11：30
地 点：普陀校区理科大楼A1514室
报告人：李竞阳 复旦大学助理教授
主持人：张心雨 华东师范大学副教授
摘 要：
Many modern datasets consist of multiple related matrices measured on a common set of units, where the goal is to recover the shared low-dimensional subspace. While the Angle-based Joint and Individual Variation Explained (AJIVE) framework provides a solution, it relies on equal-weight aggregation, which can be strictly suboptimal when views exhibit significant statistical heterogeneity (arising from varying SNR and dimensions) and structural heterogeneity (arising from individual components). In this paper, we propose HeteroJIVE, a weighted two-stage spectral algorithm tailored to such heterogeneity. Theoretically, we first revisit the ``non-diminishing" error barrier with respect to the number of views $K$ identified in recent literature for the equal-weight case. We demonstrate that this barrier is not universal: under generic geometric conditions, the bias term vanishes and our estimator achieves the $O(K^{-1/2})$ rate without the need for iterative refinement. Extending this to the general-weight case, we establish error bounds that explicitly disentangle the two layers of heterogeneity. Based on this, we derive an oracle-optimal weighting scheme implemented via a data-driven procedure. Extensive simulations corroborate our theoretical findings, and an application to TCGA-BRCA multi-omics data validates the superiority of HeteroJIVE in practice.
报告人简介：
李竞阳曾在密歇根大学从事 2博士后研究，近期即将加入复旦大学担任助理教授。他的研究兴趣集中在高维统计学领域，主要关注矩阵与张量学习、非凸优化等。李竞阳致力于为大规模数据问题开发可扩展的算法，并深入探究其理论性质。他在基于黎曼优化的张量估计方法，以及针对高维回归与低秩恢复的稳健框架等方面做出了贡献。目前，他还在探索在线学习和联邦学习领域的问题，致力于设计能够在计算效率与隐私约束之间取得平衡的自适应算法。