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A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation

Caroline Lawless 1 Julyan Arbel 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : For a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman-Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible control of the clustering behaviour. Two commonly used representations of the Pitman-Yor process are the stick-breaking process and the Chinese restaurant process. The former is a constructive representation of the process which turns out very handy for practical implementation, while the latter describes the partition distribution induced. Obtaining one from the other is usually done indirectly with use of measure theory. In contrast, we provide here an elementary proof of Pitman-Yor's Chinese Restaurant process from its stick-breaking representation.
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Submitted on : Tuesday, December 11, 2018 - 3:16:03 AM
Last modification on : Friday, February 4, 2022 - 3:23:46 AM
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Caroline Lawless, Julyan Arbel. A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation. Dependence Modeling, De Gruyter, 2019, 7 (1), pp.45-52. ⟨10.1515/demo-2019-0003⟩. ⟨hal-01950653⟩



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