KAUST Grant NumberKUS-CI-016-04
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AbstractStatistical 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. © 2012 Elsevier Inc.
CitationChakraborty S, Ghosh M, Mallick BK (2012) Bayesian nonlinear regression for large small problems. Journal of Multivariate Analysis 108: 28–40. Available: http://dx.doi.org/10.1016/j.jmva.2012.01.015.
SponsorsThe research of Bani K Mallick was supported by National Science Foundation grant DMS 0914951 and by award KUS-CI-016-04 made by King Abdullah University of Science and Technology (KAUST).
JournalJournal of Multivariate Analysis