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Thus, aposterior mean funciton of Gaussian Process $f(\mathbf{x})$ in the points of test set $X_*$ takes form:  \begin{equation}  \label{meanNoise} \label{eq:mean_noise}  \hat{f}(X_*) = K_* \left(K + \tilde{\sigma}^2 I\right)^{-1} Y,  \end{equation}  where $I$ -- identity matrix of size $(N \times N)$.