Bayesian classification using a noninformative prior and mislabeled training data

The average probability of error is used to demonstrate the performance of a Bayesian classification test (referred to as the Combined Bayes Test (CBT )) when the training data of each class are mislabeled. The CBT combines th e information in discrete training and test data to infer symbol probabilit ies, where a uniform Dirichlet prior (i.e., a noninformative prior of compl ete ignorance) is assumed for all classes. Using the CBT, classification pe rformance is shown to degrade when mislabeling exists in the training data, and this occurs with a severity that depends upon the mislabeling probabil ities. With this, it is shown that as the mislabeling probabilities increas e M*, which is the best quantization fineness related to the Hughes phenome non of pattern recognition, also increases. Notice, that even when the actu al mislabeling probabilities are known by the CBT it is not possible to ach ieve the classification performance obtainable without mislabeling. However , the negative effect of mislabeling can be diminished, with more success f or smaller mislabeling probabilities, if a data reduction method called the Bayesian Data Reduction Algorithm (BDRA) is applied to the training data. Published by Elsevier Science Ltd.