Given n observations from two balanced classes, consider the task of labeling an additional m inputs that are known to all belong to one of the two classes. Special cases of this problem are well-known: with completeknowledge of class distributions (n=∞) theproblem is solved optimally by the likelihood-ratio test; whenm=1 it corresponds to binary classification; and when m≈ n it is equivalent to two-sample testing. The intermediate settings occur in the field of likelihood-free inference, where…