A marginal sampler for $σ$-Stable Poisson-Kingman mixture models
This work addresses computational challenges in Bayesian nonparametrics for statisticians and data scientists, presenting an incremental improvement in sampling efficiency.
The paper tackles inference in Bayesian nonparametric mixture models using σ-stable Poisson-Kingman random probability measures, introducing a novel MCMC sampling scheme with fixed auxiliary variables per iteration and demonstrating its efficiency in density estimation and clustering tasks compared to competing methods.
We investigate the class of $σ$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor process, the normalized inverse Gaussian process and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of $σ$-stable Poisson-Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for making inference in Bayesian nonparametric mixture modeling. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a fixed number of auxiliary variables per iteration. We apply our sampling scheme for a density estimation and clustering tasks with unidimensional and multidimensional datasets, and we compare it against competing sampling schemes.