A Training Sample Size Estimation for the Bayes Classifier

This paper presents a theoretical training sample size estimation for the Bayes classifier based on the estimation of a learning curve for the class-conditional probability density. A statistic proportional to the posterior probability of the true class is defined. This allows the convergence of the statistic to be dependent only on the training sample size and the feature vector dimension. Thus, the estimated learning curve is general and independent of the model parameters and can be used to estimate the error probability for a given training sample size. Several simulations are included for multivariate Gaussian distributions demonstrating the fitting of the curve to estimate the reduction of error by increasing the training sample size.