Naive Credal Classifier 2: a robust approach to classification for small and incomplete data sets

Naive Credal Classifier, which is an imprecise-probability counterpart of Naive Bayes, is rigorously extended to a very general and flexible treatment of incomplete data, yielding a new classifier called Naive Credal Classifier 2 (NCC2). The new classifier delivers classifications that are robust to the presence of small sample sizes and missing values. In particular, some empirical evaluations show how, by issuing set-valued classifications, NCC2 is able to isolate, and properly deal with instances that are hard to classify (on which Naive Bayes’ accuracy drops considerably), and to perform as well as Naive Bayes on the others. The experiments point also to a more general problem: they show that with missing values the empirical evaluations may not reliably estimate the accuracy of a traditional classifier, such as Naive Bayes. This appears to add even more value to the robust approach to classification implemented by NCC2. keywords: Naive Bayes; Naive Credal Classifier; Imprecise Probabilities; Missing Values; Conservative Inference Rule; Missing At Random.