  Many machine learning problems can be characterized by mutual contamination
models. In these problems, one observes several random samples from different
convex combinations of a set of unknown base distributions. It is of interest
to decontaminate mutual contamination models, i.e., to recover the base
distributions either exactly or up to a permutation. This paper considers the
general setting where the base distributions are defined on arbitrary
probability spaces. We examine the decontamination problem in two mutual
contamination models that describe popular machine learning tasks: recovering
the base distributions up to a permutation in a mixed membership model, and
recovering the base distributions exactly in a partial label model for
classification. We give necessary and sufficient conditions for identifiability
of both mutual contamination models, algorithms for both problems in the
infinite and finite sample cases, and introduce novel proof techniques based on
affine geometry.
