Oversampling of under-represented data is a way to combat class imbalance. For example, if we have a training data set with 100 data points of class A and 1000 data points of class B, we can over sample the 100 A data (may be with some sophisticated oversampling methods) to generate 1000 A data to mitigate the data imbalance.
Now, let's say we have 1100 data points of class B, and class A has 2 subclasses, A1 and A2, which have 100 and 10 data points, respectively. And we are still interested in binary classification.
In this case, how should I over sample data of class A to address class imbalance? Should I over sample A1 to 1000 and A2 to 100, or over sample both A1 and A2 to 550?
Besides running an experiment, is there any theoretical analysis of this kind of class imbalance problem?