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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Bayesian hierarchical kernel machines for nonlinear regression and classification

Bayesian hierarchical kernel machines for nonlinear regression and classification

Chapter:
(p.50) 4 Bayesian hierarchical kernel machines for nonlinear regression and classification
Source:
Bayesian Theory and Applications
Author(s):

Sounak Chakraborty

Bani K Mallick

Malay Ghosh

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0004

This chapter introduces Bayesian kernel based methods for regression and binary classification. The chapter is organized as follows. Section 4.2 describes the general regression and classification problem under the regularization framework and discusses a reproducing kernel Hilbert space (RKHS) and its related properties. Section 4.3 gives a detailed description of Bayesian kernel machine regression models and the associated prior justification. Section 4.4 discusses the Bayesian kernel machine model for binary classification problems. Finally, some concluding remarks and future possibilities are provided in Section 4.5.

Keywords:   Bayesian kernel machine, regression models, binary classification, reproducing kernel Hilbert space

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