8d5f526a31d3731a30eb58d5874cf5b1-Supplemental-Conference.pdf

Note that given access to population of positives and unlabeled, α can be estimated as minxpupxq{pppxq. To make a prediction on test point from unlabeled data, we can then use Bayes rule to obtain the following transformation on probabilistic output ofthe domain discriminator:f " α In particular, for each classj PYs, we can first estimate its prevalencepαj in the unlabeled target. Forclassification,we can traink PU learning classifiersfi, wherefi is trained to classify a source classi versus others in target. Assuming that eachfj returns a score betweenr0,1s, during test time, an examplex is classifiedasfpxqgivenby fpxq" " Note that mathematically any OSLS problems can be thought of ask-PU problems as per(10). Put simply,for individual PU problems defined for source classesj PYs,we need existence of a sub-domainXj suchthatweonlyobserveexample forthatclassjinXj. This error incurred due to bias can be mild forasingle mixture proportion estimation taskbutaccumulates withincreasing number ofclasses (i.e.,k). Assume that there exists aunique solutionptpyq. Without loss of generality, we assume that|Xwp| " k.