Kernel PLS Regression II: Kernel Partial Least Squares Regression by Projecting Both Independent and Dependent Variables into Reproducing Kernel Hilbert Space

2018 ◽  
Author(s):  
Yan Pei
Keyword(s):  
Hilbert Space ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Pls Regression ◽  
Least Squares Regression ◽  
Kernel Partial Least Squares ◽  
Dependent Variables

scholarly journals Coefficient-Based Regression with Non-Identical Unbounded Sampling

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jia Cai
Keyword(s):  
Hilbert Space ◽  
Integral Operator ◽  
Error Analysis ◽  
Least Squares ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Least Squares Regression ◽  
Regression Problem ◽  
Novel Technique ◽  
Sample Error

We investigate a coefficient-based least squares regression problem with indefinite kernels from non-identical unbounded sampling processes. Here non-identical unbounded sampling means the samples are drawn independently but not identically from unbounded sampling processes. The kernel is not necessarily symmetric or positive semi-definite. This leads to additional difficulty in the error analysis. By introducing a suitable reproducing kernel Hilbert space (RKHS) and a suitable intermediate integral operator, elaborate analysis is presented by means of a novel technique for the sample error. This leads to satisfactory results.

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