  We compare and contrast two approaches to validating a trained classifier
while using all in-sample data for training. One is simultaneous validation
over an organized set of hypotheses (SVOOSH), the well-known method that began
with VC theory. The other is withhold and gap (WAG). WAG withholds a validation
set, trains a holdout classifier on the remaining data, uses the validation
data to validate that classifier, then adds the rate of disagreement between
the holdout classifier and one trained using all in-sample data, which is an
upper bound on the difference in error rates. We show that complex hypothesis
classes and limited training data can make WAG a favorable alternative.
