Prototype and exemplar models both use a single, fixed level of complexity in their representations of categories, with prototype models exhibiting the simplest representations, and exemplar models using the most complex representations. Treating categorization as a type of statistical inference, I describe a family of nonparametric Bayesian models of categorization based on the Dirichlet process mixture model (DPMM). These models represent categories as combinations of clusters of objects and, together, produce a continuum of representational complexities where prototype and exemplar models are special cases, occupying opposite ends of the spectrum. DPMM models allow the level of complexity of category representations to be chosen to suit the task at hand or to change over time; this flexibility can explain psychological results demonstrating that people's inferences are more congruent with prototype models at some times and exemplar models at other times.
The DPMM can be generalized into a larger framework of models based on the hierarchical Dirichlet process (HDP). The HDP subsumes the DPMM and multiple previous psychological models, including prototypes, exemplars, and the Rational Model of Categorization. In addition, the HDP contains a family of previously unexplored models which make interesting predictions about how information can be shared between multiple categories. While most other categorization models learn each individual category in isolation and independently of the others, these HDP models share information between categories. This sharing of information can improve the speed and accuracy of learning and explained certain transfer learning effects that were observed in people's judgments. I introduce an extension of the HDP, called the tree-HDP, which is designed to infer systems of hierarchically related categories. The tree-HDP is able to simultaneously learn categories at multiple levels of generality and infer the taxonomic relationships between them.