引智计划系列讲座
浏览数：0
引智计划系列讲座
时间: 07/07/2011, Thursday, 10:00 am
地点: 电信楼5-406会议室
报告人: 霍晓明, 副教授, 佐治亚理工学院工业与系统工程系
题目: Towards Completely-Drive-Driven Functional Estimation
Abstract
Suppose input variable Xi and response yi have the relation: yi = f(Xi) + ？i, where ？i are i.i.d. noises. Furthermore, we assume that Xi’s are ‘adequately’ sampled within a domain Ω and function f(·) is unknown. Estimating f(·) is called functional estimation, and is the objective for many well-known parametric and nonparametric methods. The most influential existing approach follows the following framework: (1) assume that f belongs to a predetermined functional class F; (2) Derive analytic description of the basis function of F in Ω; (3) Turn the functional estimation problem into a quadratic programming problem, for which analytical and numerical solutions are available. This approach runs into difficulty when the domain Ω is irregular, or nonstandard. We have developed a strategy that can circumvent this difficulty. In particular, a method that is completely driven by data is invented to solve the functional estimation problem. We show that nearly all good asymptotic properties of the existing state-of-the-art approaches are inherited by our data-driven approach. These properties include optimal rate of convergence, asymptotic optimality, etc. We use numerical examples to demonstrate better performance of the proposed method when the domain Ω is irregular. This is a joint work with Zhouwang Yang and Huizhi Xie.
Speaker
霍晓明，男，博士，美国佐治亚理工学院副教授。霍教授于1993年获得中国科技大学学士学位，1997年和1999年在斯坦福大学分别获得硕士和博士学位，2005年获得佐治亚理工学院SIGMA XI 青年教师奖，2006年8月任美国佐治亚理工大学工业与系统工程学院副教授。曾代表中国参加德国举行的第30界数学奥林匹克竞赛，并获金奖。主要研究领域为：计算金融、图像处理、小波理论、多尺度方法论（multiscale methodology）等。是IEEE高级会员，IPAM会员，在IEEE Transactions on Information Theory等顶级杂志上发表多篇论文，并有很高的引用率。最近三年连续获得美国国家自然科学基金资助项目。此外，从2008年起受邀在上海交通大学主讲stochastics等方面的课程。霍教授的详细情况：http://www.isye.gatech.edu/faculty-staff/profile.php?entry=xh9
时间: 07/07/2011, Thursday, 10:00 am
地点: 电信楼5-406会议室
报告人: 霍晓明, 副教授, 佐治亚理工学院工业与系统工程系
题目: Towards Completely-Drive-Driven Functional Estimation
Abstract
Suppose input variable Xi and response yi have the relation: yi = f(Xi) + ？i, where ？i are i.i.d. noises. Furthermore, we assume that Xi’s are ‘adequately’ sampled within a domain Ω and function f(·) is unknown. Estimating f(·) is called functional estimation, and is the objective for many well-known parametric and nonparametric methods. The most influential existing approach follows the following framework: (1) assume that f belongs to a predetermined functional class F; (2) Derive analytic description of the basis function of F in Ω; (3) Turn the functional estimation problem into a quadratic programming problem, for which analytical and numerical solutions are available. This approach runs into difficulty when the domain Ω is irregular, or nonstandard. We have developed a strategy that can circumvent this difficulty. In particular, a method that is completely driven by data is invented to solve the functional estimation problem. We show that nearly all good asymptotic properties of the existing state-of-the-art approaches are inherited by our data-driven approach. These properties include optimal rate of convergence, asymptotic optimality, etc. We use numerical examples to demonstrate better performance of the proposed method when the domain Ω is irregular. This is a joint work with Zhouwang Yang and Huizhi Xie.
Speaker
霍晓明，男，博士，美国佐治亚理工学院副教授。霍教授于1993年获得中国科技大学学士学位，1997年和1999年在斯坦福大学分别获得硕士和博士学位，2005年获得佐治亚理工学院SIGMA XI 青年教师奖，2006年8月任美国佐治亚理工大学工业与系统工程学院副教授。曾代表中国参加德国举行的第30界数学奥林匹克竞赛，并获金奖。主要研究领域为：计算金融、图像处理、小波理论、多尺度方法论（multiscale methodology）等。是IEEE高级会员，IPAM会员，在IEEE Transactions on Information Theory等顶级杂志上发表多篇论文，并有很高的引用率。最近三年连续获得美国国家自然科学基金资助项目。此外，从2008年起受邀在上海交通大学主讲stochastics等方面的课程。霍教授的详细情况：http://www.isye.gatech.edu/faculty-staff/profile.php?entry=xh9