# An elementary derivation of the Chinese restaurant process from Sethuraman's stick-breaking process

arXiv: https://arxiv.org/abs/1801.00513 · HTML: https://mlsanity.com/paper/1801.00513/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Distributed Collapsed Gibbs Sampler for Dirichlet Process Mixture Models in Federated Learning](https://mlsanity.com/paper/2312.11169/) (2023)

## Abstract (arXiv)

The Chinese restaurant process (CRP) and the stick-breaking process are the two most commonly used representations of the Dirichlet process. However, the usual proof of the connection between them is indirect, relying on abstract properties of the Dirichlet process that are difficult for nonexperts to verify. This short note provides a direct proof that the stick-breaking process leads to the CRP, without using any measure theory. We also discuss how the stick-breaking representation arises naturally from the CRP.