Bayesian multiple response kernel regression model for high dimensional data and its practical applications in near infrared spectroscopy

Sounak Chakraborty

Computational Statistics & Data Analysis, 2012, vol. 56, issue 9, 2742-2755

Abstract: Non-linear regression based on reproducing kernel Hilbert space (RKHS) has recently become very popular in fitting high-dimensional data. The RKHS formulation provides an automatic dimension reduction of the covariates. This is particularly helpful when the number of covariates (p) far exceed the number of data points. In this paper, we introduce a Bayesian nonlinear multivariate regression model for high-dimensional problems. Our model is suitable when we have multiple correlated observed response corresponding to same set of covariates. We introduce a robust Bayesian support vector regression model based on a multivariate version of Vapnik’s ϵ-insensitive loss function. The likelihood corresponding to the multivariate Vapnik’s ϵ-insensitive loss function is constructed as a scale mixture of truncated normal and gamma distribution. The regression function is constructed using the finite representation of a function in the reproducing kernel Hilbert space (RKHS). The kernel parameter is estimated adaptively by assigning a prior on it and using the Markov chain Monte Carlo (MCMC) techniques for computation.

Keywords: Bayesian prediction; Laplace distribution; Metropolis–Hastings algorithm; Near infrared spectroscopy; Reproducing kernel Hilbert space; Nonlinear regression; Vapnik’s ϵ-insensitive loss (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947312001016
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:9:p:2742-2755

DOI: 10.1016/j.csda.2012.02.019

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().