Editing Cross-validation (statistics) (section)

==Computational issues==

Most forms of cross-validation are straightforward to implement as long as an implementation of the prediction method being studied is available.  In particular, the prediction method can be a "black box" – there is no need to have access to the internals of its implementation.  If the prediction method is expensive to train, cross-validation can be very slow since the training must be carried out repeatedly.  In some cases such as [[least squares]] and [[kernel regression]], cross-validation can be sped up significantly by pre-computing certain values that are needed repeatedly in the training, or by using fast "updating rules" such as the [[Sherman–Morrison formula]].  However one must be careful to preserve the "total blinding" of the validation set from the training procedure, otherwise bias may result.  An extreme example of accelerating cross-validation occurs in [[linear regression]], where the results of cross-validation have a [[closed-form expression]] known as the ''prediction residual error sum of squares'' ([[PRESS statistic|PRESS]]).