报告人：马平教授, 佐治亚大学

报告题目：Efficient computation of smoothing splines via adaptive basis sampling

报告时间：2014年12月19日，周五，14:30开始

报告地点：学院南路校区中财大厦二层通用教室一

报告人人简介：

佐治亚大学（UGA）统计系教授，美国普渡大学统计学博士，哈佛大学统计系博士后。马平教授在非参数统计、数据建模、超大样本统计等方面有着很深的理论造诣，在高水平学术杂志上发表论文20余篇，承担9项美国国家科学基金（NSF）科研项目。曾获得Canadian Journal of Statistics优秀论文奖、美国自然科学基金CAREER 奖。University of Illinois优秀教师，同时担任Journal of the American Statistical Association等多个国际著名统计学期刊的副主编。

报告摘要：

Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large data sets has hindered their wide application.

In this talk, I present a new method, named adaptive basis sampling, for efficient com- putation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O(n3). We achieve a more scalable computation in multivariate case by evaluatingthe smoothing spline using a smaller set of basis functions, are obtained by an adaptive sampling scheme that utilizes values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as the full basis smoothing splines. Using simulation studies and a large scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a previous sampling method that does not use the values of response variable.

[编辑]：孙颖