流形拓展t-过程回归  

A manifold extended t-process regression

作　　者：郭世威 王占锋[1] 吴耀华[1] Guo Shiwei;Wang Zhanfeng;Wu Yaohua(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2021年第5期382-389,403,共9页JUSTC

基　　金：supported by the National Natural Science Foundation of China(11971457);the Anhui Provincial Natural Science Foundation(1908085MA06);the Fundamental Research Funds for the Central Universities(WK2040000035).

摘　　要：本文提出了一种流形拓展t-过程回归模型,用来分析带有复杂协变量的函数型数据.该流形拓展t-过程回归模型可将协变量数据变换至特征空间,然后用拓展t-过程回归将特征空间数据转换到观测数据空间,从而对观测数据进行建模.我们建立了一个估计程序来估计模型中的参数.对真实数据和模拟数据进行了分析,结果说明所提流形拓展t-过程回归模型是可行的.A manifold extended t-process regression(meTPR)model is developed to fit functional data with a complicated input space.A manifold method is used to transform covariate data from input space into a feature space,and then an extended t-process regression is used to map feature from feature space into observation space.An estimation procedure is constructed to estimate parameters in the model.Numerical studies are investigated with both synthetic data and real data,and results show that the proposed meTPR model performs well.

关 键 词：高斯过程回归 拓展t-过程回归 流形 稳健性 

分 类 号：O212.7[理学—概率论与数理统计]