How to deal with highly skewed (on counts) dependent variables? I am working on a binary classification problem and the dataset consists of several variables which are count variables. For example, how many times a customer defaulted on a broadband bill payment in the last 3 months. 

The problem is, these features are highly skewed. This is how the distribution for the above variable looks like:

0.0     98.175855
1.0      1.275902
2.0      0.348707
3.0      0.199535


This is due to the nature of the event being evaluated during the construction of the feature. For example, the majority of the population may not have defaulted hence the value is 0 for 98% of them.

There are several such variables and they are measuring important events. Therefore I cannot remove these variables. However, I am afraid the model would not be learning anything from these features as there is very less information in them.

Questions:


Am I right in assuming these features will not be useful to the model in the current state?
How can these features be handled?
What models will you employ?

If you are working with deep learning, you can train it using mini batch gradient descent, and "artificially" build each mini batch so that the classes you want to predict appear with a more balanced frequency.