  This paper begins with a general theory of error in cross-validation testing
of algorithms for supervised learning from examples. It is assumed that the
examples are described by attribute-value pairs, where the values are symbolic.
Cross-validation requires a set of training examples and a set of testing
examples. The value of the attribute that is to be predicted is known to the
learner in the training set, but unknown in the testing set. The theory
demonstrates that cross-validation error has two components: error on the
training set (inaccuracy) and sensitivity to noise (instability). This general
theory is then applied to voting in instance-based learning. Given an example
in the testing set, a typical instance-based learning algorithm predicts the
designated attribute by voting among the k nearest neighbors (the k most
similar examples) to the testing example in the training set. Voting is
intended to increase the stability (resistance to noise) of instance-based
learning, but a theoretical analysis shows that there are circumstances in
which voting can be destabilizing. The theory suggests ways to minimize
cross-validation error, by insuring that voting is stable and does not
adversely affect accuracy.
