Why positive-unlabeled learning? Machine learning can be divided into several areas: supervised learning, unsupervised learning, semi-supervised learning, learning to rank, recommendation systems, etc, etc.

One such area is PU Learning, where only Positive and Unlabeled instances are available.

There are many publications about this, usually involving a lot of mathematics...

When looking at the literature, I was expecting to see methods similar to self-training (from semi-supervised learning), where labels are adjusted gradually according to the classifier margins.

I don't think these is what practitioners from the area do, and I was unable to navigate the mathematics or to find a survey on PU learning.

Could someone from the area perhaps clarify what said practitioners do? Why can they not just use a binary classifier where the negative class=unlabeled? Can negative labels exist among the unlabeled data? What is the goal and what metrics exist to evaluate said goal?
A couple of points I have since found myself:


I was right in suspecting that self-training could be used for PU learning. In fact, I found the original paper on PU Learning, and indeed the paper is a variation on self-training. (Oddly enough, the original authors had Positive, Unlabeled and Negative examples!)
The authors of this survey identify three families of methods: (i) two-step strategy (identify reliable negative examples in the unlabeled data and then use supervised learning), (ii) weight the positive and unlabeled
examples, and estimate the conditional probability of positive label given an example (I believe this is akin to semi-supervised self-training), and (iii) just treat the unlabeled data as highly noisy negative data.
There are also some interesting loss functions to be used with neural networks (and I imagine could be adapted for gradient boosting) described in Table 1 of this paper.