I am currently exploring PU learning. This is learning from positive and unlabeled data only. One of the publications [Zhang, 2009] asserts that it is possible to learn by modifying the loss function of an algorithm of a binary classifier with probabilistic output (for example Logistic Regression). Paper states that one should optimize Balanced Accuracy.
Vowpal Wabbit currently supports five loss functions [listed here]. I would like to add a custom loss function where I optimize for AUC (ROC), or equivalently, following the paper: 1 - Balanced_Accuracy.
I am unsure where to start. Looking at the code reveals that I need to provide 1st, 2nd derivatives and some other info. I could also run the standard algorithm with Logistic loss but trying to adjust l1 and l2 according to my objective (not sure if this is good). I would be glad to get any pointers or advices on how to proceed.
UPDATE More search revealed that it is impossible/difficult to optimize for AUC in online learning: answer