报告题目：A Duality Framework for Analyzing Function Regression

报告人： 吴磊 北京大学

报告时间：12月12日 上午10:00-11:00

报告地点：五教5505

摘要：

In this talk, we investigate the sample complexity of learning a function class in the noiseless regime, an important yet underexplored area in classical statistical learning theory. By leveraging tools from information-based complexity (IBC), we establish a dual equivalence between approximation and estimation, which enables us to derive sample complexity estimates using tools from approximation theory. To demonstrate the power of our duality framework, we explore two important but less-examined problems: random feature learning beyond the kernel regime and L^\infty learning in reproducing kernel Hilbert spaces. To formalize the duality, we introduce a new concept of IBC, termed I-complexity, to measure the size of a function class. Notably, I-complexity provides a tight characterization of learning in noiseless settings and holds potential for broad applications in learning analysis across more scenarios.

个人简介：

吴磊现为北京大学数学学院和机器学习研究中心助理教授，研究方向为深度学习理论。他于2012年获南开大学数学与应用数学专业学士学位，2018年毕业于北京大学计算数学专业，2018年11月至2021年10月先后在美国普林斯顿大学和宾夕法尼亚大学从事博士后研究。