Distributed least squares prediction for functional linear regression*

被引:6
作者
Tong, Hongzhi [1 ]
机构
[1] Univ Int Business & Econ, Sch Stat, Beijing 100029, Peoples R China
基金
中国国家自然科学基金;
关键词
distributed learning; functional linear model; reproducing kernel Hilbert space; least squares regression; unlabeled data; MINIMAX; RATES;
D O I
10.1088/1361-6420/ac4153
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
To cope with the challenges of memory bottleneck and algorithmic scalability when massive data sets are involved, we propose a distributed least squares procedure in the framework of functional linear model and reproducing kernel Hilbert space. This approach divides the big data set into multiple subsets, applies regularized least squares regression on each of them, and then averages the individual outputs as a final prediction. We establish the non-asymptotic prediction error bounds for the proposed learning strategy under some regularity conditions. When the target function only has weak regularity, we also introduce some unlabelled data to construct a semi-supervised approach to enlarge the number of the partitioned subsets. Results in present paper provide a theoretical guarantee that the distributed algorithm can achieve the optimal rate of convergence while allowing the whole data set to be partitioned into a large number of subsets for parallel processing.
引用
收藏
页数:22
相关论文
共 28 条
[1]  
[Anonymous], 2002, Cambridge Studies in Advanced Mathematics, DOI DOI 10.1017/CBO9780511755347
[2]  
[Anonymous], 2002, Applied Functional Data Analysis: Methods and Case Studies
[3]   THEORY OF REPRODUCING KERNELS [J].
ARONSZAJN, N .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAY) :337-404
[4]   Convergence rates of Kernel Conjugate Gradient for random design regression [J].
Blanchard, Gilles ;
Kraemer, Nicole .
ANALYSIS AND APPLICATIONS, 2016, 14 (06) :763-794
[5]   Minimax and Adaptive Prediction for Functional Linear Regression [J].
Cai, T. Tony ;
Yuan, Ming .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2012, 107 (499) :1201-1216
[6]  
Caponnetto A, 2007, FOUND COMPUT MATH, V7, P331, DOI 10.1007/S10208-006-0196-8
[7]  
Chakrabarti D, 2017, J MACH LEARN RES, V18, P1
[8]  
De Vito E, 2005, J MACH LEARN RES, V6, P883
[9]  
Engl H. W., 1996, REGULARIZATION INVER, V375
[10]  
Ferraty F., 2006, Nonparametric functional data analysis: theory and practice