A theoretical distribution analysis of synthetic minority oversampling technique (SMOTE) for imbalanced learning

Abstract Class imbalance occurs when the class distribution is not equal. Namely, one under-represented (minority class), and other has significantly more samples in data (majority class). The problem prevalent many real world applications. Generally, minority of interest. synthetic over-sampling technique (SMOTE) method considered most prominent for handling unbalanced data. SMOTE generates new patterns by performing linear interpolation between their K nearest neighbors. However, generated do necessarily conform to original distribution. This paper develops a novel theoretical analysis deriving probability samples. To best our knowledge, this first work mathematical formulation patterns’ allows us compare density with true underlying class-conditional density, order assess how representative are. derived formula verified computing it on number densities versus computed estimated empirically.