  We propose a new problem formulation which is similar to, but more
informative than, the binary multiple-instance learning problem. In this
setting, we are given groups of instances (described by feature vectors) along
with estimates of the fraction of positively-labeled instances per group. The
task is to learn an instance level classifier from this information. That is,
we are trying to estimate the unknown binary labels of individuals from
knowledge of group statistics. We propose a principled probabilistic model to
solve this problem that accounts for uncertainty in the parameters and in the
unknown individual labels. This model is trained with an efficient MCMC
algorithm. Its performance is demonstrated on both synthetic and real-world
data arising in general object recognition.
