  Multiple Instance Learning (MIL) is a weakly-supervised problem in which one
label is assigned to the whole bag of instances. An important class of MIL
models is instance-based, where we first classify instances and then aggregate
those predictions to obtain a bag label. The most common MIL model is when we
consider a bag as positive if at least one of its instances has a positive
label. However, this reasoning does not hold in many real-life scenarios, where
the positive bag label is often a consequence of a certain percentage of
positive instances. To address this issue, we introduce a dedicated
instance-based method called ProMIL, based on deep neural networks and
Bernstein polynomial estimation. An important advantage of ProMIL is that it
can automatically detect the optimal percentage level for decision-making. We
show that ProMIL outperforms standard instance-based MIL in real-world medical
applications. We make the code available.
