Theoretical and experimental study of SMOTE: limitations and comparisons
  of rebalancing strategies
Abdoulaye Sakho Erwan Scornet Emmanuel Malherbe
Synthetic Minority Oversampling Technique (SMOTE) is a common rebalancing
strategy for handling imbalanced data sets. Asymptotically, we prove that SMOTE
(with default parameter) regenerates the original distribution by simply
copying the original minority samples. We also prove that SMOTE density
vanishes near the boundary of the support of the minority distribution,
therefore justifying the common BorderLine SMOTE strategy. Then we introduce
two new SMOTE-related strategies, and compare them with state-of-the-art
rebalancing procedures. We show that rebalancing strategies are only required
when the data set is highly imbalanced. For such data sets, SMOTE, our
proposals, or undersampling procedures are the best strategies.