  In this study, we consider classification problems based on neural networks
in data-imbalanced environment. Learning from an imbalanced data set is one of
the most important and practical problems in the field of machine learning. A
weighted loss function based on cost-sensitive approach is a well-known
effective method for imbalanced data sets. We consider a combination of
weighted loss function and batch normalization (BN) in this study. BN is a
powerful standard technique in the recent developments in deep learning. A
simple combination of both methods leads to a size-mismatch problem due to a
mismatch between interpretations of effective size of data set in both methods.
We propose a simple modification to BN to correct the size-mismatch and
demonstrate that this modified BN is effective in data-imbalanced environment.
