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\begin{abstract}In \begin{abstract}  In  thistext block and begin editing. You can also click  paper we consider effect of the covariance function choice for the Gaussian Processes Regression (GPR) model. We show that the standard weighted Euclidean distance for covariance function modelling implies specific properties on the underlying data generation process which are not true in practice. We propose an efficient method for more generic covariance modelling via Mahalanobis distance. We show that proposed approach also connetected to the Sufficient Dimension Reduction (SDR) problem and provide statistical test for estimation of the effective dimension. All the main claims are supported with experimental results on artificial and real data. The impact of the dimensionality reduction with proposed approach is illustrated in the problem of aircraft engine time-to-failure prediction. \end{abstract}