An important consequence of the larger noise in the DFT/MRCI(2) potentials is that it translates into a limitation on the level of degeneracy that can be achieved. The GPR predictor returns a mean y(X * ) and standard deviation δ y (X * ) by treating the target y as a Gaussian random variable. Within the GPR framework, we can then say that the real value y(X * ) falls between the interval y(X * ) ± 2δ y (X * ) with a 95% confidence. For a noiseless GPR model, ignoring the presence of a small regularization term, the predicted variance of a training point is zero: