  In this paper we explore noise tolerant learning of classifiers. We formulate
the problem as follows. We assume that there is an ${\bf unobservable}$
training set which is noise-free. The actual training set given to the learning
algorithm is obtained from this ideal data set by corrupting the class label of
each example. The probability that the class label of an example is corrupted
is a function of the feature vector of the example. This would account for most
kinds of noisy data one encounters in practice. We say that a learning method
is noise tolerant if the classifiers learnt with the ideal noise-free data and
with noisy data, both have the same classification accuracy on the noise-free
data. In this paper we analyze the noise tolerance properties of risk
minimization (under different loss functions), which is a generic method for
learning classifiers. We show that risk minimization under 0-1 loss function
has impressive noise tolerance properties and that under squared error loss is
tolerant only to uniform noise; risk minimization under other loss functions is
not noise tolerant. We conclude the paper with some discussion on implications
of these theoretical results.
