Rule Set Complexity for Mining Incomplete Data Using Probabilistic Approximations Based on Generalized Maximal Consistent Blocks

Abstract

AbstractIn this chapter, missing attribute values in incomplete data sets have two possible interpretations: lost values and “do not care” conditions. Lost values are currently unavailable, e.g., they were erased, while “do not care” conditions are replaceable by any specified attribute value. For data mining, we use two kinds of probabilistic approximations, global and saturated. Both probabilistic approximations are constructed from maximal consistent blocks. Thus, since we use two kinds of missing attribute values and two kinds of probabilistic approximations, we use four different data mining methods. We have shown, in our previous study, that pairwise differences in an error rate, calculated by ten-fold cross validation between those four methods, are statistically insignificant (5% level of significance). Hence, we explore another problem: when the rule set complexity is the smallest. We show that the difference between using both kinds of probabilistic approximations is, in general, insignificant. However, we should explore both interpretations of missing attribute values, “do not care” conditions and lost values, since there are significant differences.