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.