Complexity of Rule Sets Mined from Incomplete Data Using Probabilistic Approximations Based on Generalized Maximal Consistent Blocks

摘要

In this paper, incomplete data sets have two kinds of missing attribute vales: lost values and “do not care” conditions. Lost values are interpreted as erased or as not inserted into the data set, while “do not care” conditions may be replaced by any specified attribute value. In addition, we use two kinds of probabilistic approximations, global and saturated. Both probabilistic approximations are constructed from generalized maximal consistent blocks. Since we are using two kinds of missing attribute values and two kinds of probabilistic approximations, we use four different ways of data mining. In our previous study, it was shown that pairwise differences in an error rate, evaluated by ten-fold cross validation between these four ways of data mining are statistically insignificant (5% level of significance). Hence, we explore the next important problem: when the rule sets will be the simplest. We show that the total number of rules is the smallest when missing attribute values are interpreted as “do not care” conditions. The difference between using both kinds of probabilistic approximations is insignificant.