Non-exchangeable random partition models for microclustering

TL;DR

This paper introduces a new class of non-exchangeable random partition models that allow for sublinear cluster size growth, providing more flexibility than traditional exchangeable models, with applications in clustering, graph generation, and real data analysis.

Contribution

The authors develop a flexible non-exchangeable partition model with controllable sublinear cluster growth, extending the applicability beyond exchangeable models like the Chinese restaurant process.

Findings

Model generates partitions with sublinear cluster size growth.

The model exhibits power-law behavior in cluster sizes.

Experiments show improved performance over traditional models.

Abstract

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensible in many cases, it has some strong implications. In particular, Kingman's representation theorem implies that the size of the clusters necessarily grows linearly with the sample size; this feature may be undesirable for some applications, as recently pointed out by Miller et al. (2015). We present here a flexible class of non-exchangeable random partition models which are able to generate partitions whose cluster sizes grow sublinearly with the sample size, and where the growth rate is controlled by one parameter. Along with this result, we provide the asymptotic behaviour of the number of clusters of a given size, and show that the model can exhibit a power-law behavior, controlled by another parameter. The construction is based on completely random measures and a Poisson embedding of the random partition, and inference is performed using a Sequential Monte Carlo algorithm. Additionally, we show how the model can also be directly used to generate sparse multigraphs with power-law degree distributions and degree sequences with sublinear growth. Finally, experiments on real datasets emphasize the usefulness of the approach compared to a two-parameter Chinese restaurant process.