  Labeling data for classification requires significant human effort. To reduce
labeling cost, instead of labeling every instance, a group of instances (bag)
is labeled by a single bag label. Computer algorithms are then used to infer
the label for each instance in a bag, a process referred to as instance
annotation. This task is challenging due to the ambiguity regarding the
instance labels. We propose a discriminative probabilistic model for the
instance annotation problem and introduce an expectation maximization framework
for inference, based on the maximum likelihood approach. For many probabilistic
approaches, brute-force computation of the instance label posterior probability
given its bag label is exponential in the number of instances in the bag. Our
key contribution is a dynamic programming method for computing the posterior
that is linear in the number of instances. We evaluate our methods using both
benchmark and real world data sets, in the domain of bird song, image
annotation, and activity recognition. In many cases, the proposed framework
outperforms, sometimes significantly, the current state-of-the-art MIML
learning methods, both in instance label prediction and bag label prediction.
