The nature of statistical learning theory
The nature of statistical learning theory
Support vector machines, reproducing kernel Hilbert spaces, and randomized GACV
Advances in kernel methods
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Variational relevance vector machines
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Computational Statistics & Data Analysis
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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 @e-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.