Advances in Kernel Regression and Function Approximation

Kernel methods constitute a proper framework to tackle regression problems that encompass fitting and regularization. This chapter considers two particularly interesting ways of treating the regression problem: based on discriminative kernel regression, and based on generative Bayesian nonparametric...

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Bibliographic Details
Published in:Digital Signal Processing with Kernel Methods pp. 333 - 385
Main Authors: Rojo-Álvarez, José Luis, Martínez-Ramón, Manel, Muñoz-Mar&iacute, Jordi, Camps-Valls, Gustau
Format: Book Chapter
Language:English
Published: Chichester, UK Wiley 2018
John Wiley & Sons, Ltd
Edition:1
Series:Wiley - IEEE
Subjects:
Bayesian nonparametric kernel regression models
Gaussian process regression algorithms
MATLAB
multi‐output function approximation
relevance vector machine
semi‐supervised support vector regression
signal processing
Support vector machines
Training
IEEE Sections
Signal processing algorithms
Function approximation
Kernel
Standards
ISBN:9781118611791, 1118611799
Online Access:Get full text
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Summary:Kernel methods constitute a proper framework to tackle regression problems that encompass fitting and regularization. This chapter considers two particularly interesting ways of treating the regression problem: based on discriminative kernel regression, and based on generative Bayesian nonparametric regression. Both families have found wide application in signal processing. For the support vector regression (SVR)‐based regression approaches, the chapter details an SVR version for multi‐output function approximation, a kernel‐based regression to cope with signal and noise dependencies (KSNR), and the semi‐supervised SVR (SS‐SVR) to incorporate the wealth of unlabeled samples in the regression function. It also summarizes some important achievements in the field of Bayesian nonparametrics and focused on the relevance vector machine (RVM) and different developments of Gaussian process regression (GPR) algorithms. The chapter further gives empirical evidence on synthetic and real examples of the presented methods. In addition, it provides some worked examples, tutorials, and pointers to useful toolboxes in MATLAB for selected methods.
ISBN:9781118611791
1118611799
DOI:10.1002/9781118705810.ch8