  An empirical investigation of the interaction of sample size and
discretization - in this case the entropy-based method CAIM (Class-Attribute
Interdependence Maximization) - was undertaken to evaluate the impact and
potential bias introduced into data mining performance metrics due to variation
in sample size as it impacts the discretization process. Of particular interest
was the effect of discretizing within cross-validation folds averse to outside
discretization folds. Previous publications have suggested that discretizing
externally can bias performance results; however, a thorough review of the
literature found no empirical evidence to support such an assertion. This
investigation involved construction of over 117,000 models on seven distinct
datasets from the UCI (University of California-Irvine) Machine Learning
Library and multiple modeling methods across a variety of configurations of
sample size and discretization, with each unique "setup" being independently
replicated ten times. The analysis revealed a significant optimistic bias as
sample sizes decreased and discretization was employed. The study also revealed
that there may be a relationship between the interaction that produces such
bias and the numbers and types of predictor attributes, extending the "curse of
dimensionality" concept from feature selection into the discretization realm.
Directions for further exploration are laid out, as well some general
guidelines about the proper application of discretization in light of these
results.
