1 research outputs found
On collapsed representation of hierarchical Completely Random Measures
The aim of the paper is to provide an exact approach for generating a Poisson
process sampled from a hierarchical CRM, without having to instantiate the
infinitely many atoms of the random measures. We use completely random
measures~(CRM) and hierarchical CRM to define a prior for Poisson processes. We
derive the marginal distribution of the resultant point process, when the
underlying CRM is marginalized out. Using well known properties unique to
Poisson processes, we were able to derive an exact approach for instantiating a
Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs
sampling strategies for hierarchical CRM models based on Chinese restaurant
franchise sampling scheme. As an example, we present the sum of generalized
gamma process (SGGP), and show its application in topic-modelling. We show that
one can determine the power-law behaviour of the topics and words in a Bayesian
fashion, by defining a prior on the parameters of SGGP.Comment: 11 pages, 1 figur