Mixture proportion estimation is the following problem: given a random sample
from a distribution $F$, and another random sample from a distribution $H$,
find
the largest value $v$ such that $F = (1-v) G + v H$, for some distribution
G. I will argue that mixture proportion estimation can be applied to several
problems in machine learning where class labels are uncertain or unavailable,
including anomaly detection, classification with label noise, classification
with sampling bias, classification with reject option, and learning with
partial
labels.