Consider a classification problem where we do not have access to labels forindividual training examples, but only have average labels over subpopulations.We give practical examples of this setup and show how such a classificationtask can usefully be analyzed as a weakly supervised clustering problem. Wepropose three approaches to solving the weakly supervised clustering problem,including a latent variables model that performs well in our experiments. Weillustrate our methods on an analysis of aggregated elections data and anindustry data set that was the original motivation for this research.
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