The cost associated with manually labeling every individual instance in large datasets is prohibitive. Significant labeling efforts can be saved by assigning a collective label to a group of instances (a bag). This setup prompts the need for algorithms that allow labeling individual instances (instance annotation) based on bag-level labels. Probabilistic models in which instance-level labels are latent variables can be used for instance annotation. Brute-force computation of instance-level label probabilities is exponential in the number of instances per bag due to marginalization over all possible combinations. Existing solutions for addressing this issue include approximate methods such as sampling or variational inference. This paper proposes a discriminative probability model and an expectation maximization procedure for inference to address the instance annotation problem. A key contribution is a dynamic programming solution for exact computation of instance probabilities in quadratic time. Experiments on bird song, image annotation, and two synthetic datasets show a significant accuracy improvement by 4%–14% over a recent state-of-the-art rank loss SIM method.