Bayesian nonlinear regression for large p small n problems

Sounak Chakraborty, Malay Ghosh and Bani K. Mallick

Journal of Multivariate Analysis, 2012, vol. 108, issue C, 28-40

Abstract: Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik’s ϵ-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models.

Keywords: Bayesian hierarchical model; Empirical Bayes; Gibbs sampling; Markov chain Monte Carlo; Metropolis–Hastings algorithm; Near infrared spectroscopy; Relevance vector machine; Reproducing kernel Hilbert space; Support vector machine; Vapnik’s ϵ-insensitive loss (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2012.01.015

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