  Most generative models for clustering implicitly assume that the number of
data points in each cluster grows linearly with the total number of data
points. Finite mixture models, Dirichlet process mixture models, and
Pitman--Yor process mixture models make this assumption, as do all other
infinitely exchangeable clustering models. However, for some applications, this
assumption is inappropriate. For example, when performing entity resolution,
the size of each cluster should be unrelated to the size of the data set, and
each cluster should contain a negligible fraction of the total number of data
points. These applications require models that yield clusters whose sizes grow
sublinearly with the size of the data set. We address this requirement by
defining the microclustering property and introducing a new class of models
that can exhibit this property. We compare models within this class to two
commonly used clustering models using four entity-resolution data sets.
