  Given only positive (P) and unlabeled (U) data, PU learning can train a
binary classifier without any negative data. It has two building blocks: PU
class-prior estimation (CPE) and PU classification; the latter has been well
studied while the former has received less attention. Hitherto, the
distributional-assumption-free CPE methods rely on a critical assumption that
the support of the positive data distribution cannot be contained in the
support of the negative data distribution. If this is violated, those CPE
methods will systematically overestimate the class prior; it is even worse that
we cannot verify the assumption based on the data. In this paper, we rethink
CPE for PU learning-can we remove the assumption to make CPE always valid? We
show an affirmative answer by proposing Regrouping CPE (ReCPE) that builds an
auxiliary probability distribution such that the support of the positive data
distribution is never contained in the support of the negative data
distribution. ReCPE can work with any CPE method by treating it as the base
method. Theoretically, ReCPE does not affect its base if the assumption already
holds for the original probability distribution; otherwise, it reduces the
positive bias of its base. Empirically, ReCPE improves all state-of-the-art CPE
methods on various datasets, implying that the assumption has indeed been
violated here.
