统计与大数据研究院准聘副教授代文林与2023届毕业生宋妍博士、阿卜杜拉国王科技大学Marc G. Genton教授在统计学顶级期刊Journal of the American Statistical Association发表合作论文。该论文研究大规模高斯过程回归模型的低秩近似问题，揭示了低秩近似过程中的节点选择与相依结构估计对预测结果渐近性质的影响，并给出了最优节点选择策略。
论文概述
Low-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified.
作者介绍
代文林，中国人民大学统计与大数据研究院预聘副教授。2008年于北京理工大学统计系获学士学位，2014年于香港浸会大学统计系获博士学位，2015年-2018年于沙特阿卜杜拉国王科技大学进行博士后研究。2018年9月加入中国人民大学统计与大数据研究院。他的主要研究方向为非参数统计、复杂数据分析与应用统计，以主要作者身份在Journal of the American Statistical Association，Journal of Machine Learning Research, Statistical Science, Technometrics, Statistica Sinica, Journal of Computational and Graphical Statistics等国际一流统计与机器学习学期刊上发表论文30余篇。曾获得泛华统计协会(International Chinese Statistical Association) 2016年国际大会颁发的Young Researcher Award.
宋妍，2023年6月毕业于中国人民大学统计与大数据研究院，目前在沙特阿卜杜拉国王科技大学进行博士后研究。研究兴趣：时空统计、子抽样方法、非参数统计、统计计算与超算技术，以主要作者身份在Journal of the American Statistical Association, Technometrics, Journal of Agricultural, Biological, and Environmental Statistics等国际一流统计学期刊上发表论文8篇。荣获国际计算机学会(Association for Computing Machinery, ACM)的2024年戈登•贝尔气候建模奖提名(ACM Gordon Bell Prize for Climate Modelling, Finalist).
