  The accuracy of machine learning systems is a widely studied research topic.
Established techniques such as cross-validation predict the accuracy on unseen
data of the classifier produced by applying a given learning method to a given
training data set. However, they do not predict whether incurring the cost of
obtaining more data and undergoing further training will lead to higher
accuracy. In this paper we investigate techniques for making such early
predictions. We note that when a machine learning algorithm is presented with a
training set the classifier produced, and hence its error, will depend on the
characteristics of the algorithm, on training set's size, and also on its
specific composition. In particular we hypothesise that if a number of
classifiers are produced, and their observed error is decomposed into bias and
variance terms, then although these components may behave differently, their
behaviour may be predictable.
  We test our hypothesis by building models that, given a measurement taken
from the classifier created from a limited number of samples, predict the
values that would be measured from the classifier produced when the full data
set is presented. We create separate models for bias, variance and total error.
Our models are built from the results of applying ten different machine
learning algorithms to a range of data sets, and tested with "unseen"
algorithms and datasets. We analyse the results for various numbers of initial
training samples, and total dataset sizes. Results show that our predictions
are very highly correlated with the values observed after undertaking the extra
training. Finally we consider the more complex case where an ensemble of
heterogeneous classifiers is trained, and show how we can accurately estimate
an upper bound on the accuracy achievable after further training.
