Regression on the basis of nonstationary Gaussian processes with Bayesian regularization

We consider the regression problem, i.e. prediction of a real valued function. A Gaussian process prior is imposed on the function, and is combined with the training data to obtain predictions for new points. We introduce a Bayesian regularization on parameters of a covariance function of the process, which increases quality of approximation and robustness of the estimation. Also an approach to modeling nonstationary covariance function of a Gaussian process on basis of linear expansion in parametric functional dictionary is proposed. Introducing such a covariance function allows to model functions, which have non-homogeneous behaviour. Combining above features with careful optimization of covariance function parameters results in unified approach, which can be easily implemented and applied. The resulting algorithm is an out of the box solution to regression problems, with no need to tune parameters manually. The effectiveness of the method is demonstrated on various datasets.