scholarly journals Reproducing Kernel Hilbert Spaces Regression and Classification Methods

Author(s):  
Osval Antonio Montesinos López ◽  
Abelardo Montesinos López ◽  
Jose Crossa

AbstractThe fundamentals for Reproducing Kernel Hilbert Spaces (RKHS) regression methods are described in this chapter. We first point out the virtues of RKHS regression methods and why these methods are gaining a lot of acceptance in statistical machine learning. Key elements for the construction of RKHS regression methods are provided, the kernel trick is explained in some detail, and the main kernel functions for building kernels are provided. This chapter explains some loss functions under a fixed model framework with examples of Gaussian, binary, and categorical response variables. We illustrate the use of mixed models with kernels by providing examples for continuous response variables. Practical issues for tuning the kernels are illustrated. We expand the RKHS regression methods under a Bayesian framework with practical examples applied to continuous and categorical response variables and by including in the predictor the main effects of environments, genotypes, and the genotype ×environment interaction. We show examples of multi-trait RKHS regression methods for continuous response variables. Finally, some practical issues of kernel compression methods are provided which are important for reducing the computation cost of implementing conventional RKHS methods.

2013 ◽  
Vol 11 (05) ◽  
pp. 1350020 ◽  
Author(s):  
HONGWEI SUN ◽  
QIANG WU

We study the asymptotical properties of indefinite kernel network with coefficient regularization and dependent sampling. The framework under investigation is different from classical kernel learning. Positive definiteness is not required by the kernel function and the samples are allowed to be weakly dependent with the dependence measured by a strong mixing condition. By a new kernel decomposition technique introduced in [27], two reproducing kernel Hilbert spaces and their associated kernel integral operators are used to characterize the properties and learnability of the hypothesis function class. Capacity independent error bounds and learning rates are deduced.


2014 ◽  
Vol 9 (4) ◽  
pp. 827-931 ◽  
Author(s):  
Joseph A. Ball ◽  
Dmitry S. Kaliuzhnyi-Verbovetskyi ◽  
Cora Sadosky ◽  
Victor Vinnikov

2009 ◽  
Vol 80 (3) ◽  
pp. 430-453 ◽  
Author(s):  
JOSEF DICK

AbstractWe give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and nonperiodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.


2017 ◽  
Vol 87 (2) ◽  
pp. 225-244 ◽  
Author(s):  
Rani Kumari ◽  
Jaydeb Sarkar ◽  
Srijan Sarkar ◽  
Dan Timotin

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