Bayesian additive regression kernels

Bayesian additive regression kernels (BARK) is a non-parametric statistics model for regression and classificationcite web| title= Bayesian Additive Regression Kernels |url= http://stat.duke.edu/people/theses/OuyangZ.html |Author = Zhi Ouyang |Publisher = Duke University] . The unknown mean function is represented as a weighted sum of kernel functions, which is constructed by a prior using
alpha-stable Levy random fields. This leads to a specification of a joint prior distribution for the number of kernels, kernel regression coefficients and kernel location parameters. It can be shown cite web| title= Bayesian Additive Regression Kernels |url= http://stat.duke.edu/people/theses/OuyangZ.html |Author = Zhi Ouyang |Publisher = Duke University] that the alpha-stable prior onthe kernel regression coefficients may be approximated by t distributions. With a heavy tail prior distribution on the kernel regression coefficients and a finite support on the kernel location parameter, BARK achieves sparse representations. The shape parameters in the kernel functions capture the non-linear interactions of the variables, which can be used for feature selection. A reversible jump Markov chain Monte Carlo algorithm is developed to make posterior inference on the unknown mean function, and the R package is available on CRANcite web| title= bark R package on CRAN |url= http://cran.r-project.org/web/packages/bark/index.html] .For binary classification using a probit link, the model can be augmented with latent normal variables and hence the same method for Gaussian noise applies in the classification problem.

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