Inconsistency of Pitman-Yor process mixtures for the number of components
arXiv:1309.0024
Abstract
In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).
This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.2708
References in corpus (1)
Cited by in corpus (9)
- Bayesian cluster analysis: Point estimation and credible balls
- Discussion on Bayesian Cluster Analysis: Point Estimation and Credible Balls by Sara Wade and Zoubin Ghahramani
- Infinite Mixtures of Infinite Factor Analysers
- Clustering consistency with Dirichlet process mixtures
- How Many Communities Are There?
- Distributed Bayesian clustering using finite mixture of mixtures
- Nested Dirichlet models for unsupervised attack pattern detection in honeypot data
- A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation
- Bayesian mixture models (in)consistency for the number of clusters