Foundation of Mining Class-Imbalanced Data

Mining class-imbalanced data is a common yet challenging problem in data mining and machine learning. When the class is imbalanced, the error rate of the rare class is usually much higher than that of the majority class. How many samples do we need in order to bound the error of the rare class (and the majority class)? If the misclassification cost of the class is known, can the costweighted error be bounded as well? In this paper, we attempt to answer those questions with PAC-learning. We derive several upper bounds on the sample size that guarantee the error on a particular class (the rare and majority class) and the cost-weighted error, with the consistent and agnostic learners. Similar to the upper bounds in traditional PAC learning, our upper bounds are quite loose. In order to make them more practical, we empirically study the pattern observed in our upper bounds. From the empirical results we obtain some interesting implications for data mining in real-world applications. As far as we know, this is the first work providing theoretical bounds and the corresponding practical implications for mining class-imbalanced data with unequal cost.