  This work explores the effects of relevant and irrelevant boolean variables
on the accuracy of classifiers. The analysis uses the assumption that the
variables are conditionally independent given the class, and focuses on a
natural family of learning algorithms for such sources when the relevant
variables have a small advantage over random guessing. The main result is that
algorithms relying predominately on irrelevant variables have error
probabilities that quickly go to 0 in situations where algorithms that limit
the use of irrelevant variables have errors bounded below by a positive
constant. We also show that accurate learning is possible even when there are
so few examples that one cannot determine with high confidence whether or not
any individual variable is relevant.
