  When selecting a classification algorithm to be applied to a particular
problem, one has to simultaneously select the best algorithm for that dataset
\emph{and} the best set of hyperparameters for the chosen model. The usual
approach is to apply a nested cross-validation procedure; hyperparameter
selection is performed in the inner cross-validation, while the outer
cross-validation computes an unbiased estimate of the expected accuracy of the
algorithm \emph{with cross-validation based hyperparameter tuning}. The
alternative approach, which we shall call `flat cross-validation', uses a
single cross-validation step both to select the optimal hyperparameter values
and to provide an estimate of the expected accuracy of the algorithm, that
while biased may nevertheless still be used to select the best learning
algorithm. We tested both procedures using 12 different algorithms on 115 real
life binary datasets and conclude that using the less computationally expensive
flat cross-validation procedure will generally result in the selection of an
algorithm that is, for all practical purposes, of similar quality to that
selected via nested cross-validation, provided the learning algorithms have
relatively few hyperparameters to be optimised.
