Efficiency of learning with imperfect supervision

摘要

We consider the problem of supervision errors in training samples in two-group discriminant analysis based on normal distributions. Using a model for training sample misclassification, we derive Efron's Asymptotic Relative Efficiency (ARE) of the discriminant function estimated under this model, relative to the case when classification is perfect. We tabulate this ARE for certain values of the Mahalanobis distance between the groups and for various levels of supervision errors. We show that training samples are useful even if prone to a certain amount of misclassification. Our formulae and tables give, for a training sample prone to a certain amount of error, sample size equivalent to that of one error-free training sample as well as that of an unsupervised sample, the equivalence being in terms of estimation efficiency.