Adaptive Bayesian classification using noninformative Dirichlet priors

A model is developed to illustrate the effect that adapting correctly labeled training data with possibly incorrectly labeled data has on classification performance. The model is based on a previously developed model for mislabeled training data that uses the uniform Dirichlet distribution as a noninformative prior on the symbol probabilities of each class. Two versions of the model are developed under different a priori mislabeling assumptions for the data. In the first case, the probability of mislabeling is fixed and known, and in the second, the mislabeling is marginalized out, given it is a priori uniformly distributed from zero to one-half. A formula for the average probability of error is used to illustrate results that are plotted as a function of the quantization complexity, and for varying numbers of adapted mislabeled data. In general, it is shown that even for severe mislabeling, performance improves as more data are adapted to the training set