学术报告报告主题: Data-Driven Kernel Matrix Computations: Geometric Analysis and Scalable Algorithms
报 告 人: Difeng Cai 助理教授
报告时间：2025年6月5日（星期四）下午17:30-18:15
报告地点：37号楼3A01
邀 请 人: 温焕尧教授
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数学学院
2025年6月3日
报告摘要：
Dense kernel matrices arise in a broad range of disciplines, such as potential theory, molecular biology, statistical machine learning, etc. To reduce the computational cost, low-rank or hierarchical low-rank techniques are often used to construct an economical approximation to the original matrix. In this talk, we consider general m-by-n kernel matrices associated with possibly high dimensional data. We perform analysis to provide a straightforward geometric interpretation that answers a central question: what kind of subset is preferable for skeleton low-rank approximations. Based on the theoretical findings, we present scalable and robust algorithms for approximating general kernel matrices that arise in astrophysics, kernel ridge regression, Gaussian processes, etc. The efficiency and robustness will be demonstrated through extensive experiments for various datasets, kernels and dimensions.
报告人介绍：
Difeng Cai received his math BS from University of Science and Technology of China and math PhD from Purdue University. He joined the math department in Southern Methodist University as an assistant professor after postdoc study at Emory University. His research focuses on developing efficient algorithms for numerical linear algebra, the adaptive solution of partial differential equations, uncertainty quantification and machine learning.