Robust Bayes classifiers

Naive Bayes classifiers provide an efficient and scalable approach to supervised classification problems. When some entries in the training set are missing, methods exist to learn these classifiers under some assumptions about the pattern of missing data. Unfortunately, reliable information about the pattern of missing data may be not readily available and recent experimental results show that the enforcement of an incorrect assumption about the pattern of missing data produces a dramatic decrease in accuracy of the classifier. This paper introduces a Robust Bayes Classifier (rbc) able to handle incomplete databases with no assumption about the pattern of missing data. In order to avoid assumptions, the rbc bounds all the possible probability estimates within intervals using a specialized estimation method. These intervals are then used to classify new cases by computing intervals on the posterior probability distributions over the classes given a new case and by ranking the intervals according to some criteria. We provide two scoring methods to rank intervals and a decision theoretic approach to trade off the risk of an erroneous classification and the choice of not classifying unequivocally a case. This decision theoretic approach can also be used to assess the opportunity of adopting assumptions about the pattern of missing data. The proposed approach is evaluated on twenty publicly available databases.