Models for Categorical Response Variables

2009 ◽  
pp. 329-393
Author(s):  
Helge Toutenburg ◽  
Shalabh
Keyword(s):  
Categorical Response ◽  
Response Variables

scholarly journals Support Vector Machines and Support Vector Regression

2022 ◽  
pp. 337-378
Author(s):  
Osval Antonio Montesinos López ◽  
Abelardo Montesinos López ◽  
Jose Crossa
Keyword(s):  
Support Vector Machines ◽  
Plant Breeding ◽  
Genomic Prediction ◽  
Kernel Functions ◽  
Support Vector ◽  
Continuous Response ◽  
Support Vector Classifier ◽  
Vector Machines ◽  
Categorical Response ◽  
Response Variables

AbstractIn this chapter, the support vector machines (svm) methods are studied. We first point out the origin and popularity of these methods and then we define the hyperplane concept which is the key for building these methods. We derive methods related to svm: the maximum margin classifier and the support vector classifier. We describe the derivation of the svm along with some kernel functions that are fundamental for building the different kernels methods that are allowed in svm. We explain how the svm for binary response variables can be expanded for categorical response variables and give examples of svm for binary and categorical response variables with plant breeding data for genomic selection. Finally, general issues for adopting the svm methodology for continuous response variables are provided, and some examples of svm for continuous response variables for genomic prediction are described.

scholarly journals Reproducing Kernel Hilbert Spaces Regression and Classification Methods

2022 ◽  
pp. 251-336
Author(s):  
Osval Antonio Montesinos López ◽  
Abelardo Montesinos López ◽  
Jose Crossa
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Statistical Machine Learning ◽  
Regression Methods ◽  
Continuous Response ◽  
Fixed Model ◽  
Kernel Hilbert Spaces ◽  
Categorical Response ◽  
Response Variables

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.

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