How to cross validate undersampling? In order to deal with an imbalanced data set I used undersampling to run a logit model. 
The question might be simple but: How do I actually cross-validate undersampling?
 A: Two interpretations:
1. How is it possible to cross validate your weights used in under sampling?
(after your further comment, I know this is not your intent) 
I don't believe you are going to have any luck answering this question. The reason for this is that cross validation is a method which is heavily based on the assumption that the distribution of data in the population is captured well in your sample, so leaving out some data from your fit and testing your model on that data should be a good proxy for how your model should fit on all the data you didn't sample.
On the other hand, under sampling is starting from the understanding that your sampled data is not representational of the true population, due to some outside information you have. Therefore, your data itself should contain no information about this bias.
2. Your weights are trusted and you want to use cross validation to build your model
In this case, there's not much you need to do: you are starting from the assumption that your new under-sampled data set is a representative sample from the true population (unlike your full dataset). As such, you can use your typical cross-validation approaches on your new under-sampled dataset. 
If you really wanted to be extra fancy (and give yourself an extra headache), you could resample from your full data set for each left-out cross validated set. Similarly, I would think using probability weights would actually be better (and so your cross validation criteria would also be weighted), but perhaps that does not mesh well with your model of choice. But for large datasets, the gains of this compared with under-sampling may be minimal enough that it's just not worth the headache. 
