Clustering and the efficient use of cognitive resources

A central component of human intelligence is the ability to make abstractions, to gloss over some details in favor of drawing out higher-order structure. Clustering stimuli together is a classic example of this. However, the crucial question remains of how one should make these abstractions—what details to retain and what to throw away? How many clusters to form? We provide an analysis of how a rational agent with limited cognitive resources should approach this problem, considering not only how well a clustering fits the data but also by how ‘complex’ it is, i.e. how cognitively expensive it is to represent. We show that the solution to this problem provides a way to reinterpret a wide range of psychological models that are based on principles from non-parametric Bayesian statistics. In particular, we show that the Chinese Restaurant Process prior, ubiquitous in rational models of human and animal clustering behavior, can be interpreted as minimizing an intuitive formulation of representational complexity.