Collective Graphical Models

There are many settings in which we wish to fit a model of the behavior of individuals but where our data consist only of aggregate information (counts or low-dimensional contingency tables). This paper introduces Collective Graphical Models—a framework for modeling and probabilistic inference that operates directly on the sufficient statistics of the individual model. We derive a highly-efficient Gibbs sampling algorithm for sampling from the posterior distribution of the sufficient statistics conditioned on noisy aggregate observations, prove its correctness, and demonstrate its effectiveness experimentally.

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